Question

A guy wire 17 feet long runs from the top of a pole to a spot on the ground. If the height of the pole is 7 feet more than the distance from the base of the pole to the spot where the guy wire is​ anchored, how tall is the​ pole?

Answer 1

The pole is 15 feet tall

Explanation:

Pythagora's Theorem

Let's call x the distance from the base of the pole to the spot where the guy wire is anchored. The height of the pole is 7 feet more, i.e. x+7.

The guy wire is 17 feet long. These dimensions form the sides of a right triangle where the guy wire is the hypotenuse.

Applying Pythagora's Theorem

`x^2+(x+7)^2=17^2`

Operating

`x^2+x^2+14x+49=289`

Rearranging and simplifying by 2

`x^2+7x-120=0`

Factoring

`(x-8)(x+15)=0`

Solving

`x=8,\ x=-15`

Only the positive solution is valid, thus x=8

The height of the pole is x+7=15 feet

The pole is 15 feet tall