There is a 10-foot long rope that is tied between a hook on the ceiling and a hook on the floor. There is no slack in the rope. Jake wants to tie up his dog, so he can do a little shopping. He detaches the rope from the floor hook and attaches the free end to the dog’s collar, which happens to be 2 feet off the floor because it’s a big dog. The dog can now run around in a circle and because the rope goes to the ceiling the dog won’t trip or get tangled up in the rope. What a good idea! What is the radius of the circle in which the dog can wander?
Answer
The dog can run in a 6-foot radius circle. To get the answer, first draw a right triangle. The long side (hypotenuse) is the length of the rope when fully stretched by the dog, 10ft. The medium side is the distance from the ceiling to the dog’s collar, 8ft. The short side of the triangle is the radius of the circle. Using the Pythagorean Theorem (a^2+b^2=c^2) we can solve for this number.
