Question

A ladder that is 20 feet tall is leaning against a building.Samuel measures that the base of the ladder touches the ground 12 feet from the base of the building.How far from the ground does the top of the ladder touch the building?

Answer 1

The distance from the ground to the top of the ladder the building is touched is 16 feet.

Explanation:

Given:

A ladder that is 20 feet tall is leaning against a building.Samuel measures that the base of the ladder touches the ground 12 feet from the base of the building.

Now, to find the distance from base of the building to the top of the ladder where building is touched.

Here, to understand the situation below is the figure attached:

Now, to get the distance from the ground to the top of the ladder where the building is touched we use pythagorean theorem:

`AB^2+BC^2=AC^2\\\\AB^2+12^2=20^2\\\\AB^2+144=400\\\\Subtracting\ both\ sides\ by\ 144\ we\ get:\\\\AB^2=256\\\\Using\ square\ root\ on\ both\ sides\ we\ get:\\\\AB=16\ feet.`

Therefore, the distance from the ground to the top of the ladder the building is touched is 16 feet.