Question

a 15 - foot ladder leans against a wall. the base of the ladder is 9 feet from the wall. how high up the wall does the ladder reach? 12 feet 24 feet 18 feet 6 feet

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 15\) feet), \(a\) is the base (\(a=9\) feet), and \(b\) is the height we want to find.
So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 15\) and \(a = 9\) into the formula:
\(b^{2}=15^{2}-9^{2}\)
\(b^{2}=225 - 81\)
\(b^{2}=144\)

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{144}\)
\(b = 12\)

Answer:

12 feet