Firefighter Practice Exam

How high does a 25-foot ladder reach when placed 6 feet from the base of a building?

1. 22 feet

2. 24.27 feet

3. 25 feet

4. 23.12 feet

The correct answer is: 24.27 feet

To determine how high a 25-foot ladder reaches when positioned 6 feet away from the base of a building, we can apply the Pythagorean theorem. The ladder, the height reached on the wall, and the distance from the base of the building form a right triangle. In this scenario, the length of the ladder represents the hypotenuse, which is 25 feet. The distance from the base of the building to the foot of the ladder is one leg of the triangle, 6 feet. We need to find the height to which the ladder reaches on the building, which is the other leg. According to the Pythagorean theorem, the relationship between the lengths of the sides in a right triangle can be expressed as follows: \(a^2 + b^2 = c^2\) Where: - \(c\) is the hypotenuse (length of the ladder = 25 feet), - \(a\) is one leg of the triangle (distance from the building = 6 feet), - \(b\) is the other leg of the triangle (height reached on the building = ?). We can rearrange this to solve for \(b\): \(b^2 = c^2