Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Let the unknown side be \(a\), \(b = \sqrt{51}\), and \(c = 10\). Then \(a^{2}+(\sqrt{51})^{2}=10^{2}\).

Step2: Simplify the equation

\(a^{2}+51 = 100\). Subtract 51 from both sides: \(a^{2}=100 - 51\).

Step3: Calculate the value of \(a^{2}\)

\(a^{2}=49\).

Step4: Find the value of \(a\)

Take the square root of both sides: \(a=\sqrt{49}\).

Answer:

\(7\)