Question

A wooden pole was broken during a windstorm. Before it broke, the total height of the pole above the ground was 50 feet. After it broke, the top of the pole touched the ground 15 feet from the base.

How tall was the part of the pole that was left standing?

Answer 1

22.75 ft

Explanation:

You want the height of the standing part of a 50 ft pole that broke so the top touches the ground 15 ft from the base.

Setup

Let x represent the height of the remaining pole. Then the part that is bent over and touching the ground has length (50 -x). The right triangle that models the geometry will have legs of 15 and x, and a hypotenuse of (50 -x). The Pythagorean theorem tells us the relationship between these lengths is ...

(50 -x)² = 15² +x²

Solution

2500 -100x +x² = 225 +x² . . . . . . . simplify the equation

2275 = 100x . . . . . . . . . . . . . . add 100x -x² -225

22.75 = x . . . . . . . . . . . . divide by 100

The part of the pole left standing is 22.75 feet high.