Geometry I need help

Question

a 18 foot wire is tied to the top of a flagpole to a stake in the ground if the stake is 6 feet from the base of the flagpole find the height of the flagpole

Answer 1

This is a common type of problem when testing if students understand how to use the Pythagorean theorem. The Pythagorean theorem is a²+b²=c². The three letter correspond to the three sides of a right, 90 degree, triangle. The two shorter sides are a and b, while the longer side (hypotenuse) that is across from he 90 degree angel is c.

If you were to draw a quick diagram for this problem you would use a right triangle where the 18 foot wire is the hypotenuse and the letters a or b can be use to represent the 6 foot distance from he flag pole.

Plugging in the lengths given into our Pythagorean equation we get:

18² = a² + 6²

Now, solve for a²:

a² = 18² - 16²

Now solve for a, get rid of the square on a by square rooting both side:

a = (18² - 16²)^1/2 ----> a = ( 324-36)^1/2 ---> a = 288^1/2 -----> 17ft

Answer 2

6² + b² = 18²

36 + b² = 324

b² = 288

b = 17 ft