Question

a ladder leans against the side of a house. the top of the ladder is 10 ft from the ground. the bottom of the ladder is 6 ft from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 6\), \(b=10\), and \(c\) is the length of the ladder.

Step2: Substitute values into the formula

Substitute \(a = 6\) and \(b = 10\) into \(a^{2}+b^{2}=c^{2}\), we get \(6^{2}+10^{2}=c^{2}\).
Calculate \(6^{2}=36\) and \(10^{2} = 100\), then \(36 + 100=c^{2}\), so \(c^{2}=136\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{136}\).
Simplify \(\sqrt{136}=\sqrt{4\times34}=2\sqrt{34}\approx 11.7\)

Answer:

\(11.7\)