Question

1. A ladder 17 feet long is leaned up against a house,

reaching a height of 15 feet. How far from the house is the

base of the ladder?

Answer 1

The base of the ladder has a length of 8 ft.

Explanation:

We have to draw a triangle, as the figure attached.

The hypothenuse of the triangle is the length of the ladder (17 ft).

The height on the wall that the ladder reach is the adjacent (15 ft).

The base of the ladder is our unknown quantity X.

We will use the Pythagorean theorem to express the relation between these numbers:

`c^2=a^2+b^2\\\\17^2=15^2+x^2\\\\x^2=17^2-15^2=289-225=64\\\\x=√(64)=8`

The base of the ladder has a length of 8 ft.