Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, if the hypotenuse is \(13\) and one leg is \(9\), then \(x^{2}+9^{2}=13^{2}\), so \(x^{2}=13^{2}-9^{2}\).

Step2: Calculate the values

First, \(13^{2}=169\) and \(9^{2}=81\). Then \(x^{2}=169 - 81=88\).

Step3: Solve for \(x\)

\(x=\sqrt{88}\approx9.38\)

Answer:

\(9.38\)