Question

a 25 - foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. will the ladder reach a window that is 21.5 feet above the ground?
no, because the ladder will only reach 20 feet high
no, because the ladder will only reach 6 feet high
yes, because the ladder will reach 20 feet high
yes, because the ladder will reach 18 feet high

Explanation:

Step1: Apply Pythagorean theorem

Let the height the ladder reaches be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 25\) (length of the ladder, hypotenuse) and \(a=15\) (distance from the base of the house). So \(h=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 25\) and \(a = 15\) into the formula: \(h=\sqrt{25^{2}-15^{2}}=\sqrt{(25 + 15)(25-15)}=\sqrt{40\times10}=\sqrt{400}=20\).

Answer:

No, because the ladder will only reach 20 feet high.