Question

A man looks up at the top of a tree. The angle of elevation is 42°. If the tree is 20 feet tall, which of the following best represents the distance from the base of the tree to where the man is standing?

A. 18.6 ft
B. 20.4 ft
C. 22.2 ft
D. 24.6 ft

Answer 1

You can draw a right triangle with theses measures:

elevation angle = 42°

base = adjacent angle = distance from the base of the three to where the man is standing.

height = opposed angle ≈ height of the tree = 20 feet.

Note: this is assuming that the elevation angle is from the ground (this is the man is looking laying on the ground).

=> tan(42) = opposed angle / adjacent side => 20 feet / x

=> x = 20 feet / tan(42) = 22.21 m

Answer: option C. 22,2 feet