Question

theorem
find the length of the leg x of the right triangle shown below.
round your answer to the nearest thousandth as needed.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 14\) cm, one leg \(b = 5\) cm, and the other leg is \(x\). So, \(x^{2}+5^{2}=14^{2}\).

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

\(x^{2}=14^{2}-5^{2}\). Calculate \(14^{2}=196\) and \(5^{2}=25\). Then \(x^{2}=196 - 25=171\).

Step3: Find the value of \(x\)

\(x=\sqrt{171}\approx 13.077\) cm.

Answer:

\(13.077\)