Question

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

Explanation:

Step1: Apply Pythagorean theorem

$$c^{2}=a^{2}+b^{2}$$
Let \(a = 8\), \(b = 4\), and \(c\) be the hypotenuse (missing side).

Step2: Substitute values

$$c^{2}=8^{2}+4^{2}$$
$$c^{2}=64 + 16$$
$$c^{2}=80$$

Step3: Simplify

$$c=\sqrt{80}$$
$$c=\sqrt{16\times5}$$
$$c = 4\sqrt{5}$$

Answer:

\(4\sqrt{5}\)