Question

A wire is to be attached to support a telephone pole. Because of surrounding buildings, sidewalks, and​ roadways, the wire must be anchored exactly 18 feet from the base of the pole. Telephone company workers have only 25 feet of​ cable, and 22 feet of that must be used to attach the cable to the pole and to the stake on the ground. How high from the base of the pole can the wire be​ attached?

Answer 1

This situation is a right triangle with the base measuring 18 and the hypotenuse 22.  We are looking for x, the height up the pole that the wire is going to be attached to.  We will use Pythagorean's Theorem to find the missing length.  $22^2-18^2=x^2$  and  $484-324=x^2$.  x^2 = 160 so x = $4 \sqrt{10}$ or 12.65 feet