Question

question
find the length of the third side. if necessary, round to the nearest tenth.
answer
attempt 1 out of 2

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\) for a right - triangle, where \(c\) is the hypotenuse. Here, if we assume the hypotenuse \(c = 9\) and one leg \(a=5\), and we want to find the other leg \(b\). Then the formula becomes \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(c = 9\) and \(a = 5\) into the formula: \(b=\sqrt{9^{2}-5^{2}}=\sqrt{81 - 25}=\sqrt{56}\).

Step3: Simplify the square root

\(\sqrt{56}=\sqrt{4\times14}=2\sqrt{14}\approx2\times3.742 = 7.484\approx7.5\)

Answer:

\(7.5\)