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 \(a = 5\) and \(b=9\) and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\).
So \(c^{2}=5^{2}+9^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(5^{2}=25\) and \(9^{2}=81\). Then \(a^{2}+b^{2}=25 + 81=106\).

Step3: Find \(c\)

Since \(c^{2}=106\), then \(c=\sqrt{106}\approx10.3\) (rounded to the nearest tenth).

Answer:

\(10.3\)