Question

solve for c

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 5\), \(b=12\).
So, \(5^{2}+12^{2}=c^{2}\).

Step2: Calculate squares

\(5^{2}=25\), \(12^{2}=144\). Then \(25 + 144=c^{2}\).

Step3: Sum and find square root

\(25+144 = 169\), so \(c^{2}=169\). Taking square root, \(c=\sqrt{169}\).

Answer:

\(13\)