Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply the Pythagorean theorem

Let the third side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 17\) (hypotenuse) and \(a = 8\) (one of the legs). So \(x^{2}+8^{2}=17^{2}\).

Step2: Simplify the equation

\(x^{2}+64 = 289\). Then \(x^{2}=289 - 64\).

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

\(x^{2}=225\).

Step4: Solve for \(x\)

\(x=\sqrt{225}\) or \(x = 15\) (since length cannot be negative).

Answer:

\(15\)