Question

you need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. how tall does the ladder need to be? 27 feet 28 feet 26 feet 25 feet

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 10\) (distance from house), \(b=25\) (height of house), and \(c\) is the length of the ladder.

Step2: Substitute values

Substitute \(a = 10\) and \(b = 25\) into the formula: \(c=\sqrt{10^{2}+25^{2}}=\sqrt{100 + 625}=\sqrt{725}\)

Step3: Simplify

\(\sqrt{725}=\sqrt{25\times29}=5\sqrt{29}\approx26.926\approx27\)

Answer:

27 feet