Question

a 12 - ft ladder leans against the side of a house. the bottom of the ladder is 7 ft from the side of the house. how high is the top of the ladder from the ground? if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the right triangle

The ladder, the house, and the ground form a right triangle. The ladder is the hypotenuse (\(c = 12\) ft), the distance from the house is one leg (\(a = 7\) ft), and the height on the house is the other leg (\(b\)) we need to find.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). We can solve for \(b\):

$$
LATEXBLOCK0
$$

Step3: Calculate the value and round

\(\sqrt{95}\approx9.7\) (rounded to the nearest tenth)

Answer:

\(9.7\)