pythagorean theorem

Question

an 18-foot tall tree is broken by the wind. the top of the tree falls and touches the ground 12 feet from its base. how many feet from the base of the tree did the break occur?

Answer 1

If the upright tree broke x feet from its base then the part that fell has a length 18-x. The triangle formed by the fallen tree obeys Pythagoras: x^2+12^2=(18-x)^2, x^2+144=324-36x+x^2, so 144=324-36x, x=(324-144)/36=180/36=5. So the tree broke 5 feet from its base.