Question

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your answer is incorrect.
for the following right triangle, find the side length x.
(right triangle with legs 15 and 8, hypotenuse x)

Explanation:

Step1: Identify the theorem

This is a right - triangle, so we use the Pythagorean theorem, which states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, the legs are \(a = 15\) and \(b = 8\), and the hypotenuse is \(x\).

Step2: Substitute the values into the formula

Substitute \(a = 15\), \(b = 8\) into the formula \(x^{2}=15^{2}+8^{2}\). Calculate \(15^{2}=225\) and \(8^{2}=64\). Then \(x^{2}=225 + 64=289\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle, we take the positive square root. So \(x=\sqrt{289}=17\).

Answer:

\(17\)