Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, hypotenuse \(c = 15\), one leg \(a = 12\), the other leg \(b = x\). So \(12^2 + x^2 = 15^2\).

Step2: Solve for \(x^2\)

Calculate \(12^2 = 144\), \(15^2 = 225\). Then \(x^2 = 225 - 144 = 81\)? Wait, no, wait, wait. Wait, no, the hypotenuse is the longest side. Wait, 15 is longer than 12, so 15 is hypotenuse. Wait, but 12 and x are legs, 15 is hypotenuse. Wait, but \(12^2 + x^2 = 15^2\), so \(x^2 = 15^2 - 12^2 = 225 - 144 = 81\)? But 81 is a perfect square, \(x = \sqrt{81} = 9\)? Wait, but that's a whole number. Wait, maybe I misread the triangle. Wait, the right angle is between 12 and x, so the hypotenuse is 15. So Pythagorean theorem: \(12^2 + x^2 = 15^2\). So \(x^2 = 225 - 144 = 81\), so \(x = \sqrt{81} = 9.00\) when rounded to nearest hundredth.

Answer:

9.00