## Geometry: Common Core (15th Edition)

The situation described forms a right triangle, where the wall and the ground are the legs and the ladder is the hypotenuse. For a right triangle, $a^2+b^2=c^2$, where a and b are the lengths of the legs and c is the length of the hypotenuse. $a^2+b^2=c^2$ Substitute the given values. $3^2+b^2=12^2$ Simplify the exponents. $9+b^2=144$ Subtract 9 from each side. $9+b^2-9=144-9$ Simplify. $b^2=135$ Take the square root of each side. $\sqrt{b^2}=\sqrt{135}$ Simplify. $b=11.6$