Question

A 6-foot ladder touches the side of a building at a point 5 feet above the ground. At what height would a 15-foot ladder touch the building if it makes the same angle with the ground as the shorter ladder?

Answer 1

The heigt is `12.5` foot.

Explanation:

Here's a simple sketch of your problem:

In both cases, your angle `alpha` is the same.

The ladder, the ground and the building build a right-angle triangle where the respective ladder is the hypotenuse.

We know that `sin` of an angle can be computed as the opposite side divided by the hypotenuse.

Thus, in the case of the `6`-foot ladder, we have:

`sin alpha = 5/6`

For the `15`-foot ladder, we have

`sin alpha = x / 15`

However, the angles are the same. Thus, we get

`5/6 = x / 15 " "<=>" " x = 5/6 * 15 = 75/6 = 12.5 " foot"`