A ladder of 14.5 meters long is leaning against the facade of a building. The base of the ladder is 10 meters away from the building. We need to find the height, in meters, that the ladder reaches on the building.

1. Problem Description

A ladder of 14.5 meters long is leaning against the facade of a building. The base of the ladder is 10 meters away from the building. We need to find the height, in meters, that the ladder reaches on the building.

2. Solution Steps

We can model this situation as a right triangle, where the ladder is the hypotenuse, the distance from the building to the base of the ladder is one leg, and the height the ladder reaches on the building is the other leg. We can use the Pythagorean theorem to find the height.

Pythagorean theorem:

$a^2 + b^2 = c^2$

where $a$ and $b$ are the lengths of the legs of a right triangle, and $c$ is the length of the hypotenuse.

In this case, $a = 10$ meters, $c = 14.5$ meters, and we want to find $b$.

$10^2 + b^2 = 14.5^2$

$100 + b^2 = 210.25$

$b^2 = 210.25 - 100$

$b^2 = 110.25$

$b = \sqrt{110.25}$

$b = 10.5$

3. Final Answer

$10.5$