A 30 ft cable extends from the floor of the lookout of a fire tower. The table is anchored from the ground 18 ft away from the base of the tower. What is the Hight of the floor of the look out tower.

Explanation:

Assume the ground is completely flat and level. We have a right triangle with hypotenuse 30, and the horizontal base leg is 18. The vertical leg is unknown, so we'll call it x.

Use the pythagorean theorem to solve for x

a^2+b^2 = c^2

x^2+18^2 = 30^2

x^2 + 324 = 900

x^2 = 900 - 324

x^2 = 576

x = sqrt(576)

x = 24

The height of the tower's floor is 24 feet.