Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, hypotenuse \(c = 13\), one leg \(a = 10\), and the other leg \(b = x\). So we have \(10^2 + x^2 = 13^2\).

Step2: Solve for \(x^2\)

Calculate \(10^2 = 100\) and \(13^2 = 169\). Then \(x^2 = 169 - 100 = 69\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x = \sqrt{69}\). Calculate \(\sqrt{69} \approx 8.31\) (rounded to the nearest hundredth).

Answer:

\(8.31\)