Question

find the length of the missing leg in the provided triangle. note that the diagram may not be to scale. 85 √85 9 √157

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Let the known legs be \(a = 6\) and the hypotenuse \(c = 11\). We want to find the other leg \(b\). So, \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 6\) and \(c = 11\) into the formula: \(b=\sqrt{11^{2}-6^{2}}=\sqrt{121 - 36}=\sqrt{85}\).

Answer:

\(\sqrt{85}\)