Question

what is the distance from the base of the house to the base of the ladder?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder \(13m\)), \(b\) is the height on the wall (\(12m\)), and \(a\) is the distance from the base of the house to the base of the ladder. We need to find \(a\), so \(a^{2}=c^{2}-b^{2}\).
Substitute \(c = 13\) and \(b = 12\) into the formula: \(a^{2}=13^{2}-12^{2}\).

Step2: Calculate \(13^{2}-12^{2}\)

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Since \(a^{2}=25\), then \(a=\sqrt{25}\).

Step3: Find the value of \(a\)

\(a = 5\) (because distance cannot be negative, we take the positive square - root).

Answer:

\(5m\)