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 wall?
what is the unknown information that could be found using the pythagorean theorem?
what is the ar
what is the hypotenuse, or length of the ladder
11.62 feet
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), \(a\) is one leg (distance from the wall), and \(b\) is the other leg (height on the wall). Here, \(c = 12\) feet and \(a=3\) feet. We need to find \(b\).

Step2: Substitute values into the formula

Substitute \(a = 3\) and \(c = 12\) into \(a^{2}+b^{2}=c^{2}\). We get \(3^{2}+b^{2}=12^{2}\), which simplifies to \(9 + b^{2}=144\).

Step3: Solve for \(b^{2}\)

Subtract 9 from both sides: \(b^{2}=144 - 9=135\).

Step4: Find \(b\)

Take the square root of \(b^{2}\). \(b=\sqrt{135}\approx11.62\) (rounded to the nearest hundredth).

Answer:

The unknown information is the leg, or height of the wall. The length of the ladder is the hypotenuse. The distance from the wall to the base of the ladder is the other leg. The height of the wall is approximately \(11.62\) feet.