1. State the problem: Compute $\cos 30^{\circ}$. 2. Formula and rules: For a right triangle $\cos(\theta)=\dfrac{\text{adjacent}}{\text{hypotenuse}}$ and in a 30-60-90 triangle the side ratios are $1:\sqrt{3}:2$. 3. Construct an equilateral triangle of side 2 and split it to form a 30-60-90 right triangle; the hypotenuse is $2$, the shorter leg is $1$ and the longer leg is $\sqrt{3}$. 4. Apply the cosine definition: $\cos 30^{\circ}=\dfrac{\text{adjacent}}{\text{hypotenuse}}=\dfrac{\sqrt{3}}{2}$. 5. Show a cancellation example when simplifying the half: $1=\dfrac{2}{2}=\dfrac{\cancel{2}}{\cancel{2}}$. 6. Final answer: $\cos 30^{\circ}=\dfrac{\sqrt{3}}{2}$.