Question

if the triangle was a right triangle and its legs were 8 and 13, what would the length of the hypotenuse be?

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 8\) and \(b=13\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}=8^{2}=64\), \(b^{2}=13^{2}=169\). Then \(a^{2}+b^{2}=64 + 169=233\).

Step3: Find the hypotenuse \(c\)

Since \(c^{2}=233\), then \(c=\sqrt{233}\).

Answer:

\(\sqrt{233}\)