Question

a right triangle is shown. what is the value of s? 6 9 12

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(a = 9\), \(c=15\), and \(b = s\). So \(9^{2}+s^{2}=15^{2}\).

Step2: Simplify the equation

\(81 + s^{2}=225\). Then \(s^{2}=225 - 81\).

Step3: Calculate \(s^{2}\)

\(s^{2}=144\).

Step4: Find \(s\)

Take the square root of both sides. Since \(s>0\) (length), \(s=\sqrt{144}\).

Answer:

C. 12