Question

find the length of the third side. if necessary, round to the nearest tenth. 13 12 answer attempt 1 out of 2

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side of a right - triangle). Here, we need to find the length of one of the legs. Let the hypotenuse \(c = 13\) and one leg \(a=12\), and the other leg be \(b\).

Step2: Rearrange the formula

We can rewrite the Pythagorean theorem as \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute the values

Substitute \(c = 13\) and \(a = 12\) into the formula: \(b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}\).

Step4: Calculate the result

\(\sqrt{25}=5\).

Answer:

5