Geometry question please help

Question

Workers accidentally drop a metal pipe that is 10 feet long. It falls into a cylindrical hole with the radius of 4 feet and a grate across the top. The pipe comes to rest leaning across the bottom of the hole. The workers are able to just reach the upper end of the pipe through the grate with a magnet at the end of a rope that is 7 feet long. About how deep is the hole.

Answer 1

The pipe will make a triangle with the bottom of the hole. The pipe itself is the hypotenuse. Since the radius of the hole is 4 feet, the bottom length of the hole is 8 feet. given this you can solve for the height of the triangle with the Pythagorean Theorem

a^2+b^2=c^2 

or in this case

8^2+b^2=10^2

once you solve for b then you add 7 feet for the length of rope.

This will give you the full height of the hole.