Question

A 12-foot ladder rests against the side of a house. The base of the ladder is 3 feet away from the side of the house. How high above the ground is the top of the ladder? Round to the nearest tenth of a foot.
a. 9.1 feet
b. 11.6 feet
c. 12.4 feet
d. 153.0 feet

Answer 1

This is a problem for the Pythagorean Theorem: a² + b² = c², where a, b, and c are the three sides of the triangle, and c is the hypotenuse. The hypotenuse of a triangle is the side across from the 90 degree angle.

In this case, the hypotenuse, c, is 12, because the ladder is 12 feet long (and is the side across from the 90 degree angle created by the ground and the side of the house). You have one of the other sides (3 feet), so you can find the last side by plugging in the numbers:

$a^2+b^2=c^2\\3^2+b^2=12^2\\9+b^2=144\\b^2=135\\\sqrt{b^2}=\sqrt{135}\\b\approx11.6 ft$