Question

a ladder that is 22 feet long is propped up against a 15 - foot - tall building. use the drop downs to answer the following questions.
what is the unknown information that could be found using the pythagorean theorem?
what measures represent each variable of the pythagorean theorem, if b is the unknown length?
( a=) ( c=)
what is the approximate length of b, rounding to the nearest hundredth?

Explanation:

Step1: Identify the values of \(a\) and \(c\)

In the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), the ladder length is the hypotenuse \(c = 22\) (the side opposite the right - angle in the right - triangle formed by the ladder, the building, and the ground), and the height of the building is \(a=15\).

Step2: Rearrange the Pythagorean theorem to solve for \(b\)

Starting with \(a^{2}+b^{2}=c^{2}\), we can isolate \(b\) as \(b=\sqrt{c^{2}-a^{2}}\).
Substitute \(a = 15\) and \(c = 22\) into the formula: \(b=\sqrt{22^{2}-15^{2}}=\sqrt{(22 + 15)(22 - 15)}\) (using the difference of squares \(x^{2}-y^{2}=(x + y)(x - y)\)).
First, calculate \((22 + 15)(22 - 15)=(37)(7)=259\). Then \(b=\sqrt{259}\approx16.09\)

Answer:

\(a = 15\), \(c = 22\), and \(b\approx16.09\)