Question

find the length of the third side. if necessary, write in simplest radical form.
3
8
answer attempt 1 out of 3
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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 legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, one leg \(a = 3\), the hypotenuse \(c = 8\), and we need to find the other leg \(b\).
Rearranging the Pythagorean theorem to solve for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 3\) and \(c = 8\) into the formula:
\(b=\sqrt{8^{2}-3^{2}}=\sqrt{64 - 9}=\sqrt{55}\)

Answer:

\(\sqrt{55}\)