A 39-foot ladder is placed against a building. The bottom of the ladder is 33 feet away from the base of the building. We need to find the height of the building.

1. Problem Description

A 39-foot ladder is placed against a building. The bottom of the ladder is 33 feet away from the base of the building. We need to find the height of the building.

2. Solution Steps

This problem can be solved using the Pythagorean theorem. The ladder, the building, and the distance from the building to the base of the ladder form a right triangle. Let $a$ be the height of the building, $b$ be the distance from the base of the building to the bottom of the ladder, and $c$ be the length of the ladder. Then, according to the Pythagorean theorem:

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

We are given that $c = 39$ feet and $b = 33$ feet. We want to find $a$. Substituting the given values into the equation:

$a^2 + 33^2 = 39^2$

$a^2 + 1089 = 1521$

$a^2 = 1521 - 1089$

$a^2 = 432$

$a = \sqrt{432}$

$a \approx 20.7846$

Rounding to the nearest tenth of a foot, we get $a \approx 20.8$ feet.

3. Final Answer

20.8