Question

find t.

12 mm

write your answer in simplest radical form.

millimeters

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=30^\circ$, opposite side is $r$, hypotenuse is $12$ mm.

Step2: Substitute values and solve

$\sin(30^\circ)=\frac{r}{12}$
Since $\sin(30^\circ)=\frac{1}{2}$, substitute:
$\frac{1}{2}=\frac{r}{12}$
Multiply both sides by 12:
$r=12\times\frac{1}{2}$

Answer:

6 millimeters