Question

A guy wire runs from the top of a cell tower to a metal stake in the ground. Santiago places a 12-foot tall pole to support the guy wire. After placing the pole, Santiago measures the distance from the stake to the pole to be 4 ft. He then measures the distance from the pole to the tower to be 20 ft. Find the length of the guy wire, to the nearest foot.​

Answer 1

Answer: We can use the Pythagorean theorem to solve this problem. Let's call the length of the guy wire "x". Then we have a right triangle with legs of 4 and 20 (the distances from the pole to the stake and tower, respectively) and hypotenuse of x (the length of the guy wire). So we can write:

4^2 + 20^2 = x^2

Simplifying the left side, we get:

16 + 400 = x^2

416 = x^2

Taking the square root of both sides (and rounding to the nearest foot), we get:

x ≈ 20.4

Therefore, the length of the guy wire is approximately 20 feet.

Explanation: