1. The problem is to find the value of $\cos 30^\circ$. 2. Recall the cosine function in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse: $$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. For special angles like $30^\circ$, we use known exact values from the unit circle or special triangles. 4. The $30^\circ$ angle corresponds to the special right triangle with angles $30^\circ$, $60^\circ$, and $90^\circ$. The sides are in ratio $1 : \sqrt{3} : 2$ where 1 is opposite $30^\circ$, $\sqrt{3}$ is adjacent to $30^\circ$, and 2 is the hypotenuse. 5. Therefore, $$\cos 30^\circ = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{\sqrt{3}}{2}$$ 6. This is the exact value of $\cos 30^\circ$. Final answer: $$\cos 30^\circ = \frac{\sqrt{3}}{2}$$