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 ar
the hypotenuse, or length of the ladder
12.37 feet
ladder
the leg, or distance from the wall to the base of the ladder
the leg, or height of the building

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 12\) feet) and \(a\) is one - leg (distance from the base of the wall, \(a=3\) feet), and \(b\) is the other leg (height of the wall). We need to find \(b\).

$$b^{2}=c^{2}-a^{2}$$

Step2: Substitute the values

Substitute \(c = 12\) and \(a = 3\) into the formula:

$$b^{2}=12^{2}-3^{2}=144 - 9=135$$

Step3: Solve for \(b\)

$$b=\sqrt{135}\approx11.62$$

Answer:

The height of the wall (the unknown information) is approximately \(11.62\) feet.