Question

A 25-foot ladder is leaning against a house with the base of the ladder 5 feet from the house. How high up the house does the ladder reach? If necessary, round to the nearest tenth foot.

Answer 1

24.5 ft

Explanation:

The Pythagorean theorem relates the lengths of the legs of a right triangle to the length of the hypotenuse. This geometry is modeled by a right triangle with one leg being 5 ft and the hypotenuse being 25 ft. Then we have (in feet), ...

25^2 = 5^2 + height^2

625 -25 = height^2 . . . . . . subtract 5^2

√600 = height ≈ 24.4949 . . . . take the square root

The ladder reaches about 24.5 ft up the house.