12 pts? Harris and Annabelle are 200 feet apart, and they are standing on opposite sides of a tree. The angles of elevation from Harris to the top of the tree is 30°, and the angle of elevation from Annabelle to the top of the tree is 35°. Find the height of the tree. Round your answer to the nearest tenth.

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Mathematics

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8 October, 12:17

12 pts? Harris and Annabelle are 200 feet apart, and they are standing on opposite sides of a tree. The angles of elevation from Harris to the top of the tree is 30°, and the angle of elevation from Annabelle to the top of the tree is 35°. Find the height of the tree. Round your answer to the nearest tenth.

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Ryker Daugherty · Answer 1

If we are to connect the root of the tree to a person to the top of the tree, we form two right triangles. If we let x and and 200 - x be the distance of Harris and Annabelle from the tree, respectively and h be the height, we form the trigonometric functions,

tan 30° = h/x

tan 35° = h / (200 - x)

The values of h and x in the equations are 63.28 ft and 109.62 ft, respectively. Thus, the answer to this item is approximately 63.28 ft.