Question

find the length of \b\ using the pythagorean theorem.

Explanation:

Step1: Recall Pythagorean Theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 40\), \(a = 24\), and we want to find \(b\). So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

\(b^{2}=40^{2}-24^{2}\)
\(b^{2}=1600 - 576\)
\(b^{2}=1024\)

Step3: Solve for \(b\)

\(b=\sqrt{1024}=32\)

Answer:

32