Question

find the length of the third side. if necessary, write in simplest radical form.
answer
attempt 2 out of 3

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 7\), \(c=\sqrt{130}\), and we need to find \(b\). Then \(b^{2}=c^{2}-a^{2}\).
Substitute the values: \(b^{2}=(\sqrt{130})^{2}-7^{2}\).

Step2: Calculate the value of \(b^{2}\)

\((\sqrt{130})^{2}-7^{2}=130 - 49\).
\(130−49 = 81\).

Step3: Find the value of \(b\)

Since \(b^{2}=81\), then \(b=\sqrt{81}\).
\(\sqrt{81}=9\).

Answer:

\(9\)