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

580 ft

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 ,

`(AB)/(AC)=(perpendicular\;side)/(hypotenuse)=sin\theta`

Substitute the values then we get

`(h)/(600)=sin75^(\circ)`

`h=60 sin75^(\circ)`

`h=579.5ft`

`h=580 ft`

Hence, the height of communication tower=580 ft