Question

find the exact value of \\( \cos x \\) in simplest radical form.

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\)

Step2: Identify the adjacent side and hypotenuse for angle \(X\)

For angle \(X\), the adjacent side to angle \(X\) is \(XY = 8\), and the hypotenuse is \(XZ=10\)

Step3: Calculate \(\cos X\)

\(\cos X=\frac{XY}{XZ}=\frac{8}{10}=\frac{4}{5}\)

Answer:

\(\frac{4}{5}\)