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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?

User Senkwich
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1 Answer

3 votes

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.

A 12-foot metal guy wire is attached to a broken stop sign to secure its position-example-1
User JosephHall
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