Question

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

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle with legs \(a = 10\), \(b = 11\) and hypotenuse \(x\), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\). So, \(x^{2}=10^{2}+11^{2}\).

Step2: Calculate \(10^{2}+11^{2}\)

\(10^{2}=100\) and \(11^{2}=121\). Then \(x^{2}=100 + 121=221\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{221}\approx14.87\)

Answer:

\(14.87\)