Question

find the length of the third side. if necessary, round to the nearest tenth.
answer attempt 1 out of 2
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Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). Here, the hypotenuse \(c = 17\) and one leg \(b = 8\), and we need to find the other leg \(a\).
Rearranging the Pythagorean theorem to solve for \(a\), we get \(a=\sqrt{c^{2}-b^{2}}\)

Step2: Substitute the values

Substitute \(c = 17\) and \(b = 8\) into the formula:
\(a=\sqrt{17^{2}-8^{2}}=\sqrt{289 - 64}=\sqrt{225}\)

Step3: Calculate the square root

\(\sqrt{225}=15\)

Answer:

15