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? 28 feet 26 feet 27 feet 25 feet

Explanation:

Step1: Apply Pythagorean theorem

The situation forms a right - triangle, where the height of the house (\(a = 25\) feet) and the distance from the house (\(b=10\) feet) are the two legs, and the ladder length (\(c\)) is the hypotenuse. The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\).

Step2: Substitute values

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

Step3: Simplify the square root

\(\sqrt{725}=\sqrt{25\times29}=5\sqrt{29}\approx5\times5.385 = 26.925\approx27\)

Answer:

27 feet