Question

solve. round to the nearest tenth. a ladder 8 m long is leaning against a building. how high on the building (in m) will the ladder reach when the bottom of the ladder is 1 m from the building?

Explanation:

Step1: Identify the problem type

This is a right - triangle problem where the ladder is the hypotenuse (\(c = 8\) m), the distance from the bottom of the ladder to the building is one leg (\(a=1\) m), 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 \(b\)

From \(a^{2}+b^{2}=c^{2}\), we get \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(a = 1\) and \(c = 8\) into the formula: \(b=\sqrt{8^{2}-1^{2}}=\sqrt{64 - 1}=\sqrt{63}\).

Step3: Calculate the value and round

\(\sqrt{63}\approx7.9\) (rounded to the nearest tenth).

Answer:

\(7.9\)