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, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 14\), \(a=11\), and \(b = x\). So, \(x^{2}+11^{2}=14^{2}\).

Step2: Rearrange the formula to solve for \(x\)

\(x^{2}=14^{2}-11^{2}\).
\(x^{2}=196 - 121\).
\(x^{2}=75\).

Step3: Take the square root of both sides

\(x=\sqrt{75}\).
\(x = 5\sqrt{3}\approx8.66\).

Answer:

\(8.66\)