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 7 ft from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth. ft

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 7\), \(b=10\), and \(c\) is the length of the ladder.

Step2: Substitute values into the formula

Substitute \(a = 7\) and \(b = 10\) into \(a^{2}+b^{2}=c^{2}\), we get \(7^{2}+10^{2}=c^{2}\).
First, calculate \(7^{2}=49\) and \(10^{2} = 100\). Then \(49 + 100=c^{2}\), so \(c^{2}=149\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{149}\approx12.2\)

Answer:

\(12.2\)