Question

When sitting atop a tree and looking down at his Pal Joey, the angle of depression of Mack’s line of sight is 53°51. If a Joey is known to be standing 25 feet from the base of the tree, how tall is the tree( to the nearest foot)? A 36 ft B 38ft C 34ft D 40ft

Answer 1

C 34ft

Explanation:

SOH CAH TOA reminds you that ...

Tan = Opposite/Adjacent

In this geometry, the height of the tree is the side Opposite the angle of elevation, with the Adjacent side being the one that is the 25 ft distance from Joey to the tree. The angles of elevation and depression are equal.

Hence ...

tan(53°51') = height/(25 ft)

height = (25 ft)·tan(53°51') ≈ 34.22 ft ≈ 34 ft.