Question

A 600-ft guy wire is attached to the top of a communications tower. If the wire makes an angle of 75° with the ground, how tall is the communications tower? (Round your answer to the nearest foot.)

Answer 1

Answer:

580 ft

Step-by-step explanation:

We are given that

Length of guy wire=600 ft

$\theta=75^{\circ}$

Let h be the height of communication tower.

In triangle ABC ,

$\frac{AB}{AC}=\frac{perpendicular\;side}{hypotenuse}=sin\theta$

Substitute the values then we get

$\frac{h}{600}=sin75^{\circ}$

$h=60 sin75^{\circ}$

$h=579.5ft$

$h=580 ft$

Hence, the height of communication tower=580 ft