Question

find the missing side.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), the formula is \(a^{2}+b^{2}=c^{2}\). Here, let the hypotenuse \(c = 15\) and one side \(a = 9\), and we want to find \(b\). Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 15\) and \(a = 9\) into the formula \(b^{2}=c^{2}-a^{2}\). So \(b^{2}=15^{2}-9^{2}=225 - 81=144\).

Step3: Solve for \(b\)

Take the square - root of both sides. Since \(b>0\) (as it represents the length of a side), \(b=\sqrt{144}=12\).

Answer:

12