Question

A 12-foot metal guy wire is attached to a broken stop sign to secure its position until repairs can be made. Attached to a stake in the ground, the guy wire makes an angle of 51˚ with the ground. How far from the foot of the stop sign is the stake, to the nearest tenth of a foot?

Answer 1

Answer: 7.6 feet.

Explanation:

1. Based on the information given in the problem, you can draw a right triangle as the one shown in the figure attached, where x is the distance between the foot of the stop sign and the stake.

2. Then, you can calculate x as following:

`cos\alpha=(adjacent)/(hypotenuse)`

Where:

`\alpha=51\°\\adjacent=x\\hypotenuse=12`

Substitute values and solve for x:

`cos(51\°)=(x)/(12)\\x=12*cos(51\°)\\x=7.55`

3. To the nearest tenth of a foot, the distance is: 7.6 feet.