Question

A 10-foot ladder is leaned against a wall. If the base of

the ladder is 3 feet from the wall, how high up the wall will
the ladder reach?

Answer 1

`√(91)` ft

Explanation:

The ladder forms a right triangle with the wall and the ground, so this question requires the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the two sides of a right triangle, and c is the diagonal/hypotenuse of the right triangle.

In this case, the two legs are the distance of the base from the wall and the wall height itself, and the hypotenuse is the size of the ladder. We need to solve for wall height. In other words:

a = 3, b = ?, c = 10

3^2 + b^2 = 10^2 --> 9 + b^2 = 100 --> b^2 = 91 --> b = sqrt(91)