Question

1. a ladder 39 feet long leans against a building and reaches the ledges of a window. if the foot of the ladder is 15 feet from the foot of building, how high is the window ledge above the ground?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 39\) feet) and \(b\) is the distance from the foot of the ladder to the building (\(b=15\) feet). Let \(a\) be the height of the window ledge above the ground. We need to solve for \(a\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 39\) and \(b = 15\) into the formula: \(a=\sqrt{39^{2}-15^{2}}=\sqrt{(39 + 15)(39 - 15)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(a=\sqrt{54\times24}=\sqrt{1296}\).

Step3: Calculate the square - root

\(\sqrt{1296}=36\).

Answer:

The window ledge is \(36\) feet above the ground.