Question

how long must a ladder be to reach the top of a 12 - foot wall if the bottom of the ladder is placed 3 feet from the base of the wall?
what is the unknown information that could be found using the pythagorean theorem?
the leg, or height of the building
what is the approximate length of the ladder needed, rounding to the nearest hundredth?
11.62 feet

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 3\) (distance from base of wall), \(b=12\) (height of wall), and \(c\) is the length of the ladder.

Step2: Substitute values into formula

Substitute \(a = 3\) and \(b = 12\) into \(c=\sqrt{a^{2}+b^{2}}\), so \(c=\sqrt{3^{2}+12^{2}}=\sqrt{9 + 144}=\sqrt{153}\).

Step3: Calculate the value

\(\sqrt{153}\approx12.37\) (rounded to the nearest hundredth).

Answer:

\(12.37\) feet