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 and \(a\) and \(b\) are the legs. Here, \(c = 40\), \(a = 24\), and we want to find \(b\). So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 40\) and \(a = 24\) into the formula \(b^{2}=c^{2}-a^{2}\). We get \(b^{2}=40^{2}-24^{2}\). Calculate \(40^{2}=1600\) and \(24^{2}=576\). Then \(b^{2}=1600 - 576=1024\).

Step3: Solve for \(b\)

Take the square root of both sides. Since \(b>0\) (as it represents a length), \(b=\sqrt{1024}=32\).

Answer:

32