Question

The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet tall. How far up the wall does the ladder reach?

Answer 1

By the Pythagorean Theorem

$$l^2=x^2+y^2$$

Given $x=3 ft, l=12ft.$

$$y=\sqrt{l^2-x^2}=\sqrt{(12)^2-(3)^2}=3\sqrt{15}\ (ft)$$

The distance the ladder reaches up the wall is $3\sqrt{15}\approx11.612$ feet.