Question

find the exact length of the missing side of the right triangle.

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Let \(a = 11\), \(c = 13\). Then \(11^{2}+b^{2}=13^{2}\).

Step2: Simplify the equation

\(121 + b^{2}=169\).
Subtract \(121\) from both sides: \(b^{2}=169 - 121\).

Step3: Calculate \(b^{2}\)

\(b^{2}=48\).

Step4: Find \(b\)

\(b=\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\).

Answer:

\(4\sqrt{3}\)