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olga nikolaevna [1]
2 years ago
6

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.
Mathematics
1 answer:
elena-s [515]2 years ago
7 0

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

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