Question

find the unknown length in the right triangle. the unknown length b in 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. Here, assume \(s\) is one leg, \(b\) is the other leg and \(19\) is the hypotenuse. So \(s^{2}+b^{2}=19^{2}\), then \(b^{2}=19^{2}-s^{2}\).

Step2: Calculate \(b\)

\(b = \sqrt{19^{2}-s^{2}}=\sqrt{361 - s^{2}}\)

Answer:

\(\sqrt{361 - s^{2}}\)