Algebra and Trigonometry (10th Edition)

Chapter 10

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4 ; Substitute the given value of hypotenuses and... more

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Apply the cofunction identity, , to the given ... more

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; Since is an acute angle, its angle will lie ... more

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; Since is an acute angle, its angle will lie ... more

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Let a right-angle triangle be ABC.The sum of two ... more

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direction ; The direction or bearing from a point... more

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The right-angle triangle can be solved by ... more

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Solving a triangle means determining the length of... more

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: ; : ; : ; Use the angle property of right angle ... more

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: ; : ; : ; Use the angle property of right-angle ... more

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: ; : ; : ; Use the angle property of right-angle ... more

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: ; : ; : ; Use the angle property of right-angle ... more

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: ; : ; : ; Use the angle property of right-angle ... more

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: ; : ; : ; Use the property of right-angle ... more

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: ; : ; : ; Use the property of right-angle ... more

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: ; : ; : ; Use the property of right-angle ... more

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: ; : ; : ; Use the right-angle triangle property... more

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: ; : ; : ; Use the right-angle triangle property... more

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: ; : ; : ; Apply the Pythagorean theorem, .... more

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: ; : ; : ; Apply the Pythagorean theorem, , ... more

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: ; : ; : ; Apply the Pythagorean theorem, , ... more

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: ; : ; : ; Apply the Pythagorean theorem, and ... more

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; ; Draw the diagram with the given value of ... more

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; ; Draw a triangle with given hypotenuse and ... more

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; ; Draw a triangle with given side and angle.... more

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; ; Draw a triangle with given side and consider ... more

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; Draw a diagram of the given data.Apply the ... more

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  ; Draw a triangle for the given information.... more

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; Calculate the length of the side opposite to ... more

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; Draw a diagrammatic representation of the given... more

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; Calculate the distance covered after 2 hours in... more

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; Convert the minutes, , into degrees. ; Find the... more

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7984 feet ; Consider the distance between the ... more

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1650 feet ; For the angle , the length of the ... more

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; The height above the wall is the difference ... more

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; The height above the player is the difference ... more

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; Draw a line from the centre of a larger circle ... more

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;  Plot the figure with the extension of lines, ... more

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;  There are two right triangles are formed by ... more

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Entire Proof Answer: Let the central angle be ... more

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Equate to 0 to determine the value of .If  is a ... more

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; Rewrite the given expression.Use the identity ... more

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; Find the value of for , , , and . ;     ; ... more

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; Write the factors of the given equation. ; ... more

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; The difference formula for sine is . For ... more

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; is an acute angle.   ; more

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; Since triangles are similar, sides must be ... more

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A triangle is said to be oblique if none of the ... more

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; The Law of Sines states that, in a triangle, ... more

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If two sides and opposite angle are given, then ... more

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The Law of Sines states that in a triangle the ... more

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ambiguous case ; Ambiguous case is when two sides ... more

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: ; : ; : ; Obtain the value of by substituting ... more

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: ; : ; : ; Obtain the value of by substituting ... more

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: ; : ; : ; Obtain the value of  by substituting ... more

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: ; : ; : ; Obtain the value of  by substituting ... more

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: ; : ; : ; Obtain the value of  by substituting  ... more

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: ; : ; : ; Obtain the value of  by substituting  ... more

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: ; : ; : ; Obtain the value of  by substituting  ... more

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: ; : ; : ; Obtain the value of  by substituting  ... more

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; ; ; Obtain the value of  by substituting  and  ... more

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; ; ; Obtain the value of  by substituting  and  ... more

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; ; ; Obtain the value of  by substituting  and  ... more

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; ; ; Obtain the value of  by substituting  and  ... more

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; ; ; Obtain the value of  by substituting  and  ... more

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; ; ; Obtain the value of  by substituting  and  ... more

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; ; ; Obtain the value of  by substituting  and ... more

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; ; ; Obtain the value of  by substituting  and  ... more

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One triangle; ; ; Substitute , , and into sine ... more

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One triangle; ; ; Substitute , , and into sine ... more

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One triangle; ; ; Substitute , , and  into sine ... more

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One triangle; ; ; Substitute , , and  into sine ... more

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No triangle ; Substitute , , and  into sine law... more

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Two triangles; ; ; ; ; Substitute , , and  into ... more

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Two triangles; ; ; ; ; Substitute , , and  into ... more

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No triangle ; Substitute , , and  into sine law... more

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No triangle ; Substitute , , and  into sine law... more

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No triangle ; Substitute , , and  into sine law... more

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Two triangles; ; ; ; ; Substitute , , and  into ... more

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Two triangles; ; ; ; ; Substitute , , and  into ... more

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; Substitute into to find the value of . ; To ... more

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; Substitute into to find the value of . ; To ... more

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; Find the value of by substituting for and ... more

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; Draw a triangle for the given information.... more

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Side 1: ; Side 2: ; Draw a triangle for given ... more

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; Let and be the distance of two runners from ... more

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; Suppose the height of tree is and the distance... more

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;  Let the length of the ramp be ft.Find by ... more

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; Draw the figure using the given information. ; ... more

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; Draw the diagram.Find the total time taken, ... more

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389,000 km ; Draw a diagram from the given ... more

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: Perpendicular length: ; Draw a diagram and take ... more

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or ; Let . Find the value of by substituting... more

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; Draw a diagram of the given data and find the ... more

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; Redraw the given figure and label the vertices ... more

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; Let be the distance between the ranger and the... more

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; Let the height of the pyramid be and the ... more

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; Let the height of Object A be and the distance... more

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187,600,000 km; 101,440,000 km ; Draw a diagram ... more

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42,300,000 km; 252,400,000 km ; Substitute , and... more

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; Considering 36 cars, calculate the angle ... more

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Entire Proof Answer:  ; Rewrite the Law of Sines... more

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Entire Proof Answer:  ; Rewrite the Law of Sines... more

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Entire Proof Answer:  ; Rewrite the Law of Sines... more

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Entire Proof Answer:   ; Rewrite the given ... more

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Entire Proof Answer:  ; Let  be the diameter of ... more

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The problem with , , and will result in one ... more

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Apply the angle sum property of a triangle to find... more

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Use the Law of Sines to find the angle opposite to... more

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1818 meters; use only right triangle geometry, ... more

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; ; 3 ; Calculate the possible rational factors of... more

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; Substitute , , , and into the distance formula... more

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; The value of for , suppose and , where is the... more

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To plot the function , stretch the graph of the ... more

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; Apply the distance formula to find the distance... more

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; According to the given condition, is an acute ... more

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Cosines ; When three sides of a triangle are given... more

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Consider the triangle in which side , angle , and... more

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Consider the triangle in which side , , and the ... more

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A triangle is said to be completely solved when ... more

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The law of cosines states that the difference of ... more

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The Law of Cosines states that .If the triangle is... more

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; ; ; To obtain the value of , substitute , , and... more

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;  ; ; To obtain the value of , substitute , , and... more

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; ; ; Use the law of cosines, .Substitute 2 for , ... more

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; ; ; Use the law of cosines, .Substitute 2 for , ... more

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; ; ; Use the law of cosines, .Substitute 6 for , ... more

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; ; ; Use the law of cosines, .Substitute 8 for , ... more

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; ; ; Use the law of cosines, .Substitute 9 for , ... more

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; ; ; Use the law of cosines, .Substitute 4 for , ... more

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; ; ; To obtain the value of , substitute , , and... more

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; ; ; Use the law of cosines, .Substitute 2 for , ... more

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; ; ; Use the law of cosines, .Substitute 1 for , ... more

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; ; ; Use the law of cosines, .Substitute 6 for... more

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; ; ; Use the law of cosines, .Substitute 3 for , ... more

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; ; ; Use the law of cosines, .Substitute 4 for , ... more

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; ; ; Use the law of cosines, .Substitute 2 for , ... more

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; ; ; Use the law of cosines, .Substitute 3 for , ... more

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; ; ; Find the value of  by substituting12 for , ... more

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; ; ; Find the value of  by substituting 4 for , 5... more

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; ; ; Use the law of cosines, . Substitute 2 for... more

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; ; ; Find the value of  by substituting 3 for , 3... more

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; ; ; Find the value of  by substituting 5 for , 8... more

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; ; ; Find the value of  by substituting 4 for , 3... more

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; ; ; Find the value of  by substituting 10 for , ... more

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; ; ; Find the value of  by substituting 9 for , 7... more

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; ; ; To obtain the value of angle, substitute ... more

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; ; ; To obtain the value of angle , substitute ... more

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; ; ; To obtain the value of angle , substitute... more

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; ; ; To obtain the value of , substitute , , and... more

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; ; ; To obtain the value of , substitute and ... more

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; ; ; To obtain the value of , substitute , , and... more

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; ; ; ; ; Substitute for , 3 for , and 10 for ... more

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; ; ; Sum of interior angles of triangle is , that... more

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; ; ; Draw a triangle using the given information... more

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; ; ; Use the law of cosines, .Substitute 10 for... more

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165 yards ; Substitute 150 for , 35 for , and for... more

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Right wire: ; Left wire: ; The angle of ... more

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; Let be the distance from the home plate to the... more

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; Let be the distance from the third base to the... more

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; Let be the distance between the two footings. ... more

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Entire Proof Answer: Use the law of cosines.  Form... more

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Entire Proof Answer: Use the law of cosines.Use ... more

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Entire Proof Answer: Use the double angle property... more

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Entire Proof Answer: Use the Law of Cosines.  Use ... more

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Entire Proof Answer:  ; Use the Law of Cosines: , ... more

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Use the Law of Cosine to find the remaining side ... more

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Use the Law of Cosine at least two times and then ... more

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The applied problem is,A triangular parcel of ... more

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Use the Law of Sines or Law of cosine depending on... more

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The Law of cosines states that the sum of the ... more

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Add and subtract 6 from the numerator of the given... more

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; ; Use the property,  to find the solution of the... more

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; ; ; ; By using trigonometric ratio, find the ... more

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; If the graph of a function is odd and passing ... more

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; The area of the triangle, , with base, , and ... more

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; The area of the triangle, , with the included ... more

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; The area of the triangle, , is , where a,b, and... more

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The area of the triangle, , is , where a and b  ... more

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Draw a triangle with sides , , and , and included ... more

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To find the area of the triangle, , use the Heron'... more

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; Apply the formula of the area for the given ... more

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3 ; Apply  the formula of the area for the given ... more

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; Apply the formula of the area for the given ... more

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; Apply the formula of the area for the given ... more

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; Apply the heron's formula for the given values ... more

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; Apply the heron's formula for the given values ... more

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; Apply the heron's formula for the given values ... more

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; Apply the heron's formula for the given values ... more

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; Apply the formula of the area for the given ... more

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; Apply the formula of the area for the given ... more

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; Apply the formula of the area for the given ... more

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; Apply the formula of the area for the given ... more

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; Apply the formula of the area for the given ... more

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; Apply the formula of the area for the given ... more

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30 ; Apply the heron's formula for the given ... more

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6 ; Apply the heron's formula for the given values... more

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; Apply the heron's formula for the given values ... more

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; Apply the heron's formula for the given values ... more

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; Apply the heron's formula for the given values ... more

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; Apply the heron's formula for the given values ... more

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Entire Proof Answer:Apply the law of Sines to find... more

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Entire Proof Answer: Find the value of using the ... more

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; Since the sum of all angles of a triangle is , ... more

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; Since the sum of all angles of a triangle is , ... more

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; Since the sum of all angles of a triangle is... more

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; Since the sum of all angles of a triangle is , ... more

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; Since the sum of all angles of a triangle is , ... more

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; Since the sum of all angles of a triangle is , ... more

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; Multiply by  to convert the angle in radians... more

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; Multiply 40 by  to convert the angle in radians... more

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; Since the three sides are given, use the Heron'... more

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; The radius of canvas is half of the diameter... more

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; The home plate is made of a rectangle and a ... more

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; Find the area of semicircle by substituting ... more

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; Draw the diagram of the given information.Find ... more

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; Draw the diagram for the given values.Find the ... more

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; Since the three sides are given, use the Heron'... more

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442,816 square miles ; Since the three sides are ... more

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; The area of the region is divided into 3 parts.... more

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;  The area of the region is divided into 3 parts... more

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Entire Proof Answer: Add the length of the sides ... more

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Entire Proof Answer: \[K=\frac{1}{2}h_1a\),  ... more

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Entire Proof Answer: Equate both areas, and find ... more

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; To find the area of the triangle, use the ... more

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Entire Proof Answer: Substitute for , for , for... more

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Entire Proof Answer: Use the trigonometric ... more

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Entire Proof Answer:  ; Use the formula, , ... more

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Entire Proof Answer: Find the area of the triangle... more

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Find the value of altitude using the trigonometric... more

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Find the semi-perimeter, and then, use the formula... more

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The area of the triangle is the product of the ... more

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Maximum value; 17 ; Comparing the given equation ... more

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; The domain of a rational function, , is all ... more

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; ; ; ; ; ; The value of  is  and the value of  is... more

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Entire Proof Answer:  ; Apply the reciprocal ... more

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; Compare the given equation with the general ... more

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simple ; The given equation is of the form of ... more

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simple ; Simple harmonic motion of an object is a ... more

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Assess the equations of simple harmonic motion,  ... more

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; At time , the object is released, the object is... more

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; At time , the object is released, the object is... more

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; At time , the object is released, the object is... more

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; At time , the object is released, the object is... more

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; As the motion is positive in upward direction ... more

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; As the motion is positive in upward direction ... more

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; Since the object is pulled down, the value of  ... more

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; Since the object is pulled down, the value of  ... more

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The displacement is obtained by multiplying the ... more

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The displacement is obtained by multiplying the ... more

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The displacement is obtained by multiplying the ... more

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The displacement is obtained by multiplying the ... more

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Plot the graphs of and . ; Form a table for and... more

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Plot the graphs of and . ; Form a table for and... more

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Plot the graphs of and . ; Form a table for and... more

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Plot the graphs of and . ; Form a table for and... more

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Plot the graphs of and . ; Form a table for and... more

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Plot the graphs of and . ; Form a table for and... more

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Plot the graphs of and . ; Form a table for and... more

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Plot the graphs of and . ; Form atable for and ... more

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; ; Apply the frequency formula, .Substitute 520 ... more

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; Since the rider should be at the lowest ... more

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; ; Apply the frequency formula, .Substitute 440 ... more

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; ; Apply the frequency formula, .Substitute for... more

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Enter the sound equation, which is produced by the... more

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Enter the sound equation, which is produced by the... more

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Amplitude: ; Period: , frequency: ; From the given... more

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Amplitude: ; Period: , frequency: ; From the given... more

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When approaches 0, approaches 1. ; Enter the ... more

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It is observed from all the graphs that the graphs... more

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It can be observed from all the graphs that as the... more

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The repetitive to and fro motion of an object ... more

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; Use the addition property of logarithmic ... more

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; ; ; Substitute for into the theorem for the ... more

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; ; ; Substitute 2 for and 5 for into the ... more

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; ;  ; Draw the triangle that represents all the ... more

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; ; ; Draw the triangle that represents all the ... more

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No triangle ; Substitute 3 for , 1 for , and for... more

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; ; ; Draw the triangle that represents all the ... more

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; ; ; Draw the triangle that represents all the ... more

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No triangle ; Substitute 2 for , 3 for , and 1 for... more

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; ; ; Substitute 10 for , 7 for , and 8 for into ... more

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; ; ; Substitute 1 for , 3 for , and for into ... more

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; ; ; Substitute 5 for , 3 for , and for into ... more

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; ; ; Substitute 1 for , for and for into the ... more

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; ; ; ; ; Substitute 3 for , 4 for and for into ... more

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; ; ; Substitute for and for in to find values... more

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; ; ; Substitute for , 5 for and 4 for into the ... more

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; Substitute 2 for , 3 for , and for into the ... more

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; Substitute 10 for , 4 for , and  for  into the ... more

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; Substitute 4 for, 3 for , and 5 for  into the ... more

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; Substitute 4 for , 2 for , and 5 for  into the ... more

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; Apply the property, which states that the sum ... more

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; Let angle be the angle of inclination of the ... more

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; Draw a figure to represent the given situation... more

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; Draw a figure to represent the given situation... more

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; Label the given figure to represent the given ... more

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; Draw a figure using the given information and ... more

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; Draw a figure using the given information and ... more

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; Illustrate the given information in the form of... more

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;  The motion of the coiled spring is simple ... more

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 Let , , and . Take random values of and ... more

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;  Let be the angle formed by the ladder with ... more

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; Since 1 mile is equal to 5280 feet, multiply 5 ... more

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; ; ; Use the Law of Cosines,  , to find side   .... more

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; ; ; Use the fact that the sum of the angles in a... more

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; ; ; Use the Law of Cosines, , to find the angle... more

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; ; ; Use the fact that sum of all the angles in a... more

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No triangle ; As one angle and two sides are given... more

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; ; ; As two sides and one angle is given, the Law... more

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; As two sides and one angle is given, use the ... more

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; Since all the three sides of the triangle are ... more

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; The difference between the area of the ... more

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; Divide the given quadrilateral into two ... more

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; The required distance is distance  . Let it be.... more

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; The required area is the sum of the area of the... more

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Side 1: ; Side 2: ; Side 3: ; As three sides of ... more

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  ; All the resistive forces are ignored. As a ... more

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; The standard form of the equation of the circle... more

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; The given equation is not in standard form .... more

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; The standard form of the equation of the circle... more

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; Square root is defined and is a real number ... more

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Compare the given equation with the general ... more

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Rewrite the given equation. ; Compare the given ... more

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; ; ; ;  ; Substitute 20 for , 15 for  and for  ... more

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; Group the odd and even powers of  separately.... more

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-intercept: , -intercept: Symmetry: NoVertical ... more

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; Apply the property , if .  ; Apply the change ... more

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; Apply the logarithmic property .  ; Convert the... more

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The first plane right triangle is , and the second... more

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;  Refer to the figure of the spherical triangle ... more

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; Write the expressions obtained in part (2). ; ... more

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; Apply the Pythagorean Theorem in triangle to ... more

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Entire Proof Answer:Apply the sine ratio and ... more

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; ; Find the angle between GF and L by applying ... more

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; ; Find the angle between GF and L by applying ... more

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; Add the distance travelled from GF to L and ... more

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City GF to city LEM: City LEM to city LEW: The ... more

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