At a certain time of day, the angle of elevation is 40°. To the nearest foot, find the height of a tree whose shadow is 31 feet long.

Question

asked Oct 11, 2022 228k views

1 Answer

Akbar Ahmed · Answer 1 · 2022-10-16T05:31:10+0000

Answer: Height of tree = 26 ft

Make a triangle ABC with 40 degrees angle. The shadow is the base of the triangle equals 31 feet.

Base = AC = 31

Perpendicular = CB = ?

Hypotenuse = AB

Using trigonometric equation

tan 40 (deg) = CB / AC

CB = Tan 40 x AC

CB = 0.83909 x 31

CB = 26.011

Thus the height of the tree = 26 ft