Question

what is the length of side x?
(image of a right triangle with one leg labeled x, the other leg labeled 9, and the hypotenuse (dashed line with arrows) labeled 15. there is a ? in the triangle. below: select the best answer)

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem, which states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 15\), one leg \(b = 9\), and the other leg \(a=x\).

Step2: Apply the Pythagorean theorem

We rearrange the formula to solve for \(x\): \(x^{2}=c^{2}-b^{2}\). Substitute \(c = 15\) and \(b = 9\) into the formula: \(x^{2}=15^{2}-9^{2}\). Calculate \(15^{2}=225\) and \(9^{2}=81\). Then \(x^{2}=225 - 81=144\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{144}=12\).

Answer:

12