Question

a 15 wire is tied from the top of a pole to a stake in the ground. if the stake is 5 ft from the base of the pole find the height of the pole

Answer 1

Imagine this pole of height h sticking out of the ground.  A wire of length 15 feet connects the top of the pole to a stake in the ground which is located 5 feet from the base of the pole.  This arrangement creates a right triangle with legs h (the height of the pole), 5 ft (distance of bottom of pole from stake) and hypotenuse 15 ft.  

We can find the height of the pole (h) using either trig or the Pythagorean Theorem.  If we use the P. T., then h^2 + 5^2 = 15^2.

This results in h^2 + 5^2 = 15^2, or h^2 + 25 = 225, and so:

h^2 = 200.  Thus, h = +√200 = +10√2.

The height of the pole is 10√2 ft, or approx. 14.14 ft.