Question

find the length of the third side. if necessary, write in simplest radical form.
answer attempt 1 out of 1
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Let the two legs be \(a = 7\) and \(b = 8\), and the hypotenuse be \(c\). Then \(c=\sqrt{a^{2}+b^{2}}\).

Step2: Substitute values

Substitute \(a = 7\) and \(b = 8\) into the formula: \(c=\sqrt{7^{2}+8^{2}}=\sqrt{49 + 64}\).

Step3: Calculate the sum

\(49+64 = 113\), so \(c=\sqrt{113}\).

Answer:

\(\sqrt{113}\)