Question

a 12 ft ladder leans against the side of a house. The bottom of the ladder is 6 ft from the side of the house. how high is the top of the ladder from the ground?

Answer 1

Approximately 10.39 ft.

Explanation:

First, draw a short diagram to understand the sides of the right triangle.

The 12 foot ladder leaning against the building would be the hypotenuse and because the bottom of the ladder is 6 feet from the house, that would be the bottom leg. We are trying to figure out the leg to the left (the top of the ladder from the ground.

To solve this, we must use the converse of the Pythagorean Theorem. To do this, we can set up the following equation.

12^2 - 6^2

144 - 36 = 108

Then we must find the square root of 108, which is approximately 10.39 feet.