You are hiking along a river and see a tall tree on thhe opposite bank. You measure the angle of elevation of the top of the tree and find it to be 61 degree. You then walk 50 feet directly away from the tree and measure the angle of elevation. If the second measurement is 49.5 degree, how tall is the tree?

Explanation:

Let the height of the tree is y and the distance of tree from point B is x.

According to the diagram

x = 0.55 y ..... (1)

(50 + 0.55y) 1.17 = y ..... from equation (1)

58.5 + 0.644 y = y

0.356 y = 58.5

y = 164.3 ft

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