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, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(14\) is the hypotenuse, \(11\) is one leg, and \(x\) is the other leg. So \(x^{2}+11^{2}=14^{2}\), which can be rewritten as \(x^{2}=14^{2}-11^{2}\).

Step2: Calculate the values

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

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{75}\approx8.66\)

Answer:

\(8.66\)