Question

a ladder that is 21 feet long is propped against a building. the bottom of the ladder was placed 4 feet from the base of the building. how high up on the building does the ladder reach? round the answer to the nearest tenth of a foot.

4.1 feet
17.0 feet
20.6 feet
21.4 feet

Explanation:

Set up the Pythagorean relationship

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

$$ h^2 + 4^2 = 21^2 $$

Solve for the height

$$ h^2 + 16 = 441 $$

$$ h^2 = 425 $$

$$ h = \sqrt{425} \approx 20.6155 $$

Round to the nearest tenth

$$ h \approx 20.6\text{ feet} $$

Answer:

• (A) 4.1 feet
• (B) 17.0 feet
• (C) 20.6 feet (Correct answer)
• (D) 21.4 feet