Question

find the missing side

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 4\), \(b = 5\) and \(c\) is the hypotenuse.
So \(c^{2}=4^{2}+5^{2}\).

Step2: Calculate \(4^{2}+5^{2}\)

\(4^{2}=16\) and \(5^{2}=25\). Then \(4^{2}+5^{2}=16 + 25\).
\(16+25 = 41\). So \(c^{2}=41\), and \(c=\sqrt{41}\).

Answer:

\(\sqrt{41}\)