Question

A flagpole that was originally 24 feet tall has cracked 9 feet from the ground and has fallen as if hinged. Find

Answer 1

The top of the flag pole touched the ground 12 feet from the base.

Since it cracked 9 feet from the base, 9 is the vertical leg of the right triangle formed.  The rest of the flagpole, 24-9=15, is the hypotenuse, as it is slanted down to the ground.  The missing side is the horizontal leg, which we will call b:

9²+b²=15²
81+b²=225

Subtract 81 from both sides:
81+b²-81=225-81
b²=144

Take the square root of both sides:
√b²=√144
b=12