Question

square roots and right triangles
what is the length of the unknown leg in the right triangle?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with hypotenuse \(c\), and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Here \(c = \sqrt{113}\), \(b = 9\), and we need to find \(a\). So \(a^{2}+9^{2}=(\sqrt{113})^{2}\).

Step2: Simplify the equation

\(a^{2}+81 = 113\). Then \(a^{2}=113 - 81\).

Step3: Calculate \(a^{2}\)

\(a^{2}=32\). So \(a=\sqrt{32}\) (since length \(a>0\)).

Answer:

\(\sqrt{32}\text{ mi}\)