Question

1. a painter leans a 20-ft ladder against a building. the base of the ladder is 12 ft from the building. to the nearest foot, how high on the building does the ladder reach?

16 feet
23 feet
32 feet
8 feet

Explanation:

Step1: Identify the right triangle

The ladder, the building, and the ground form a right triangle. The ladder is the hypotenuse ($c = 20$ ft), the distance from the base of the ladder to the building is one leg ($a = 12$ ft), and the height on the building is the other leg ($b$), which we need to find. We use the Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Rearrange the formula to solve for \( b \)

We rearrange the Pythagorean theorem to solve for \( b \): \( b = \sqrt{c^2 - a^2} \).

Step3: Substitute the values

Substitute \( c = 20 \) and \( a = 12 \) into the formula: \( b = \sqrt{20^2 - 12^2} \).

Step4: Calculate the squares

First, calculate the squares: \( 20^2 = 400 \) and \( 12^2 = 144 \).

Step5: Subtract the squares

Subtract the two results: \( 400 - 144 = 256 \).

Step6: Take the square root

Take the square root of 256: \( \sqrt{256} = 16 \).

Answer:

16 feet (corresponding to the option "16 feet")