Question

finding the hypotenuse in right triangles
interpreting a real - world scenario
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 af
<
the hypotenuse, or length
of the ladder
<
the leg, or distance from
the wall to the base of the
ladder
<
the leg, or height of
the building
<
ded, rounding to the nearest hundredth?

Explanation:

Step1: Identify the formula

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 base of the wall, \(a = 3\) feet), and \(b\) is the other leg (height of the wall, which we want to find).

Step2: Substitute the values into the formula

We know \(c\) (length of the ladder) and \(a\) (distance from the base). Rearranging the formula for \(b\): \(b=\sqrt{c^{2}-a^{2}}\). Substituting \(c = 12\) and \(a = 3\), we get \(b=\sqrt{12^{2}-3^{2}}=\sqrt{144 - 9}=\sqrt{135}\).

Step3: Calculate the value

\(\sqrt{135}\approx11.62\) (rounded to the nearest hundredth).

Answer:

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