Question

find the length of the unknown side of the triangle. the length of the unknown side of the triangle is (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the unknown side be \(a\), \(b = 5\) and \(c=11\). Then \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute the values

\(a^{2}=11^{2}-5^{2}\)
\(a^{2}=121 - 25\)
\(a^{2}=96\)

Step3: Simplify the radical

\(a=\sqrt{96}=\sqrt{16\times6}\)
\(a = 4\sqrt{6}\)

Answer:

\(4\sqrt{6}\text{ m}\)