Question

A guy wire runs from the top of a cell tower to a metal stake in the ground. Penelope

places a 12-foot tall pole to support the guy wire. After placing the pole, Penelope
measures the distance from the stake to the pole to be 5 ft. She then measures the
distance from the pole to the tower to be 21 ft. Find the length of the guy wire, to the
nearest foot.

Answer 1

68 ft

Explanation:

You want the length of a guy wire from a stake to the top of a cell tower if the stake is 5 ft from a 12-ft pole that is 21 ft from the tower. The guy wire crosses the top of the pole.

Triangles

The attached diagram shows the geometry. The smaller triangle is a right triangle with legs 5 and 12. Its hypotenuse is ...

c = √(5² +12²) = √169 = 13

The larger triangle is similar and has a base of 21+5 = 26 units. This means its hypotenuse, the length of the wire, will be 26/5 times the length of the hypotenuse of the smaller triangle.

guy wire length = (26/5)(13 ft) = 67.6 ft ≈ 68 ft

The length of the guy wire is about 68 feet.