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 groun if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, where the ladder is the hypotenuse (\(c = 12\) ft), the distance from the bottom of the ladder to the house is one leg (\(a = 7\) ft), and the height from the ground to the top of the ladder 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 can rewrite the Pythagorean theorem as \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(c = 12\) and \(a=7\) into the formula: \(b=\sqrt{12^{2}-7^{2}}=\sqrt{144 - 49}=\sqrt{95}\).

Step3: Calculate the value of \(\sqrt{95}\)

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

Answer:

\(9.7\)