Question

A 26-foot rope is used to brace a tent pole at the county fair. The rope is anchored 10 feet from the box of the pole. How tall is the tent pole?

Answer 1

First, we are going to draw the situation. From our drawing we can infer that the pole, the rope, and the ground make a right triangle. Notice that the length of the rope is the hypotenuse of the triangle and the distance from the pole to the anchor point of the rope is one of the legs of the triangle. To find the other leg, the length of the pole, we are going to use the Pythagorean theorem:

`h^2=26^2-10^2`

`h^2=676-100`

`h^2=576`

`h= √(576)`

`h=24` feet

We can conclude that the pole is 24 feet tall.

Answer 2

The explanation of the problem is as shown in the figure.
So, the rope represents the hypotenuse of a right triangle.
and the tent pole is one of the legs of the right triangle.
let the length of the tent pole = x

and by using Pythagorean equation
∴ x² = 26² - 10² = 576
∴ x = √576 = 24 feet

So, the length of tent pole = 24 feet