Question

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: Apply Pythagorean theorem

For a right - triangle with legs \(a = 9\), \(b\) (unknown) and hypotenuse \(c = 13\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So, \(b^{2}=c^{2}-a^{2}\).
Substitute \(a = 9\) and \(c = 13\) into the formula: \(b^{2}=13^{2}-9^{2}\).
Calculate \(13^{2}=169\) and \(9^{2}=81\). Then \(b^{2}=169 - 81=88\).

Step2: Solve for \(b\)

Take the square root of \(b^{2}\), \(b=\sqrt{88}\).
Simplify \(\sqrt{88}=\sqrt{4\times22}=2\sqrt{22}\approx 9.4\) (rounded to the nearest tenth).

Answer:

\(9.4\)