Question

A 15 ft. telephone pole has a wire that extends from the top of the pole to the ground. The wire and the ground form a 42 angle. How long is the wire, and what is the distance from the base of the pole to the spot where the wire touches the ground?

Answer 1

The correct answer is A wire=22.4ft distance 16.7ft

Answer 2

The correct option is 1.

Explanation:

The height of the pole is 15 ft and the wire and the ground form a 42 angle.

Let the length of wire be x and the distance from the base of the pole to the spot where the wire touches the ground be y.

`\sin\theta=(Perpendicular)/(Hypotenuse)`

`\sin(42^(\circ))=(15)/(x)`

`x=(15)/(\sin(42^(\circ)))`

`x=22.417148248`

`x\approx 22.4`

Therefore the length of wire is 22.4 ft.

`\tan\theta=(Perpendicular)/(Base)`

`\tan(42^(\circ))=(15)/(y)`

`y=(15)/(\tan(42^(\circ)))`

`y=16.6591877224`

`y=16.7`

Therefore the distance from the base of the pole to the spot where the wire touches the ground is 16.7 ft.

Option 1 is correct.