Question

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

Explanation:

Step1: Use Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Let the two legs be \(a = 9\) and \(b\), and the hypotenuse \(c = 13\). We need to find \(b\). So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 9\) and \(c = 13\) into the formula: \(b^{2}=13^{2}-9^{2}\).

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Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{88}\approx9.4\)

Answer:

\(9.4\)