Question

A wire extends from the top of a building to the ground, 90 feet away from the building. The wire creates an angle of

elevation of 22 degrees with the ground. How long is the wire, to the nearest foot?
36 ft
97 ft
223 ft
90 ft

Answer 1

The correct option is 97 ft.

Explanation:

It is given that the wire is 90 feet away from the building.

The required figure is shown below:

Let the length of the wire is AC.

Here, the base is 90 feet and we need to find the value of AC.

`\cos \theta=\frac{\text{Adj}}{\text{Hyp}}`

`\cos 22^(\circ) = (BC)/(AC)`

`0.927\approx (90)/(AC)`

`AC\approx 97\text{ ft}` (nearest foot)

Hence, the correct option is 97 ft.