Question

If a person stands 40 ft from a tree and the angle of elevation made from their eyes (5 ft above the ground) to the top of the tree is 47°, how tall is the tree? Round your answer to the nearest foot.

Answer 1

Using the given information, the height of the tree is 48 ft

Trigonometry

From the question, we are to determine the height of the tree

In the given diagram, the height of the tree is (x + 5) feet

First, we will determine the value of x

tan 47° = x / 40

x = 40 × tan47°

x = 42.89 ft

∴ The height of the tree = (42.89 + 5) ft

Height of the tree = 47.89 ft

Height of the tree ≈ 48 ft

Hence, the height of the tree is 48 ft.

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