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 \(c = 6\), one leg \(a = 5\), and the other leg \(b = x\). So we have \(5^2 + x^2 = 6^2\).

Step2: Solve for \(x^2\)

Calculate \(5^2 = 25\) and \(6^2 = 36\). Then \(x^2 = 36 - 25 = 11\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x = \sqrt{11}\). Calculate \(\sqrt{11} \approx 3.32\) (rounded to the nearest hundredth).

Answer:

\(3.32\)