Question

1. a painter leans a 34-ft ladder against a building. the base of the ladder is 16 ft from the building. to the nearest foot, how high on the building does the ladder reach?

30 feet
18 feet
38 feet
26 feet

Explanation:

Step1: Identify the right triangle

The ladder, the building, and the ground form a right triangle. The ladder is the hypotenuse ($c = 34$ ft), the distance from the base of the ladder to the building is one leg ($a = 16$ ft), and the height on the building is the other leg ($b$) 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 \( c = 34 \) and \( a = 16 \) into the formula: \( b = \sqrt{34^2 - 16^2} \). First, calculate \( 34^2 = 1156 \) and \( 16^2 = 256 \). Then, \( 1156 - 256 = 900 \). So, \( b = \sqrt{900} = 30 \).

Answer:

30 feet