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

Answer:

The correct option is 1.

Step-by-step 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.

$\sin\theta=\frac{Perpendicular}{Hypotenuse}$

$\sin(42^{\circ})=\frac{15}{x}$

$x=\frac{15}{\sin(42^{\circ})}$

$x=22.417148248$

$x\approx 22.4$

Therefore the length of wire is 22.4 ft.

$\tan\theta=\frac{Perpendicular}{Base}$

$\tan(42^{\circ})=\frac{15}{y}$

$y=\frac{15}{\tan(42^{\circ})}$

$y=16.6591877224$

$y=16.7$

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.