Question

A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole. The angle of depression from the top if the pole is 43 degrees. What is the length of the wire?

Answer 1

Explanation:

angle of depression, θ = 43°

distance between the pole and the wire on the ground, d = 20 ft.

Let the length of the wire is L.

According to the diagram,

Cosθ = d / L

Cos 43 = 20 / L

0.73 = 20 / L

L = 27.35 ft

Thus, the length of the wire is 27.35 ft.

Answer 2

Length of wire = 27.35 feet

Explanation:

Refer the given figure.

The length of wire is CB.

Given that AB = 20 feet

∠ACB = 47°

We have

`sin\angle ACB=(AB)/(CB)\\\\sin47=(20)/(CB)\\\\CB=27.35feet`

Length of wire = 27.35 feet