Question

find u.

60°
u
6√3 mm
30°

write your answer in simplest radical form.

millimeters

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta=30^\circ$, adjacent side is $u$, hypotenuse is $6\sqrt{3}$.

Step2: Substitute values into formula

$\cos(30^\circ)=\frac{u}{6\sqrt{3}}$
We know $\cos(30^\circ)=\frac{\sqrt{3}}{2}$, so:
$\frac{\sqrt{3}}{2}=\frac{u}{6\sqrt{3}}$

Step3: Solve for $u$

Multiply both sides by $6\sqrt{3}$:
$u=\frac{\sqrt{3}}{2} \times 6\sqrt{3}$
Simplify: $u=\frac{6 \times 3}{2}=9$

Answer:

9 millimeters