Question

find the exact value of cos a in simplest radical form.

Explanation:

Step1: Recall cosine definition in right triangle

In a right triangle, $\cos A = \frac{\text{adjacent side to } A}{\text{hypotenuse}}$.

Step2: Identify sides for angle A

For angle \( A \), the adjacent side is \( AC = 6 \), and the hypotenuse is \( AB=\sqrt{85} \).

Step3: Calculate \(\cos A\)

Using the definition, $\cos A = \frac{AC}{AB}=\frac{6}{\sqrt{85}}$. Rationalize the denominator: $\frac{6\sqrt{85}}{85}$.

Answer:

$\frac{6\sqrt{85}}{85}$