Question

find a.
6
2\sqrt{3}
2
12

Explanation:

Step1: Use cosine function

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the adjacent side is $a$, and the hypotenuse is $4\sqrt{3}$. So, $\cos30^{\circ}=\frac{a}{4\sqrt{3}}$.

Step2: Substitute the value of $\cos30^{\circ}$

We know that $\cos30^{\circ}=\frac{\sqrt{3}}{2}$. Then $\frac{\sqrt{3}}{2}=\frac{a}{4\sqrt{3}}$.

Step3: Solve for $a$

Cross - multiply: $a=\frac{\sqrt{3}\times4\sqrt{3}}{2}$. Since $\sqrt{3}\times\sqrt{3}=3$, then $a=\frac{4\times3}{2}$.

Step4: Calculate the result

$a = 6$.

Answer:

6