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

Explanation:

Step1: Recall cosine - ratio definition

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

Step2: Identify adjacent and hypotenuse sides

For angle $A$, the adjacent side to angle $A$ is $AC = 6$, and the hypotenuse is $AB=\sqrt{37}$.

Step3: Calculate $\cos A$

$\cos A=\frac{AC}{AB}=\frac{6}{\sqrt{37}}$.

Step4: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{37}$: $\cos A=\frac{6\sqrt{37}}{37}$.

Answer:

$\frac{6\sqrt{37}}{37}$