Question

John has a 10-foot piece of rope that he wants to use to support his 8-foot tree. How far from thebase of the tree should he secure the rope?

Answer 1

The right angle triangle representing the given scenario is shown below.

From the triangle,

AB represents the height of the tree = one leg of the triangle

AC represents the length of the rope = hypotenuse of the triangle

AB = x represents the distance from the base of the tree = other leg of the triangle

We would find x by applying the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

By substituting these values into the equation, we have

10^2 = 8^2 + x^2

100 = 64 + x^2

Substracting 64 from both sides of the equation, we have

100 - 64 = 64 - 64 + x^2

36 = x^2

Taking square root of both sides,

x = 6

The rope should be 6 feet from the base