Question

Lisa tied a piece of rope to a tree branch. She is standing 5 feet away from the base of the tree, and the branch is 12 feet off the ground. The length of the rope from the tree branch to Lisa’s feet is r feet long.

Answer 1

When you draw this out, what you have is a right triangle problem.  The height of the rope from the ground is 12 (a side), the distance she is from the base of the tree is 5 (a side), and the length of the rope is the hypotenuse.  Use Pythagorean's Theorem to find the length of the hypotenuse: 5^2+12^2 = c^2 or
25+144 = c^2 and c^2 = 169, which makes the length of the rope come out to be 13 feet long.