Question

A construction worker places a 12-foot ladder up against a wall, which reaches a height on the wall of 10 feet. Approximately how many feet away from the wall is the bottom of the ladder?

A. 2 feet
B. 4.4 feet
C. 6.6 feet
D. 15.6 feet

Answer 1

The bottom of the ladder is approximately 6.6 feet away from the wall, which is determined by applying the Pythagorean theorem to calculate the missing side of the right triangle formed by the ladder, the wall, and the ground.

Step-by-step explanation:

To determine how far the bottom of the ladder is from the wall we can use the Pythagorean theorem because we are dealing with a right triangle where the ladder is the hypotenuse, the height it reaches up the wall is one leg, and the distance from the wall is the other leg. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c).

In this problem:

• the hypotenuse (c) is the length of the ladder, which is 12 feet
• one leg (a) is the height the ladder reaches on the wall, which is 10 feet
• we need to find the other leg (b), which is the distance from the wall

Using the Pythagorean theorem:

1. a² + b² = c²
2. 10² + b² = 12²
3. 100 + b² = 144
4. b² = 144 - 100
5. b² = 44
6. b = √44 ≈ 6.6 feet

So, the bottom of the ladder is approximately 6.6 feet away from the wall, which corresponds to option C.