Question

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

Explanation:

Step1: Recall cosine definition

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

Step2: Identify sides

Adjacent to $A$ is $AC = 3$, hypotenuse is $AB = \sqrt{58}$.

Step3: Compute $\cos A$

$\cos A = \frac{3}{\sqrt{58}}$. Rationalize the denominator: $\frac{3\sqrt{58}}{58}$.

Answer:

$\frac{3\sqrt{58}}{58}$