Question

find g.
right triangle with right angle at bottom left, 60° at top, 30° at bottom right, left leg labeled g, hypotenuse labeled 4√3 m
write your answer in simplest radical form.
blank meters

Explanation:

Step1: Identify trigonometric ratio

We use sine for angle $30^\circ$: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(30^\circ)=\frac{g}{4\sqrt{3}}$

Step2: Substitute $\sin(30^\circ)$ value

$\sin(30^\circ)=\frac{1}{2}$, so:
$\frac{1}{2}=\frac{g}{4\sqrt{3}}$

Step3: Solve for $g$

Multiply both sides by $4\sqrt{3}$:
$g=\frac{1}{2} \times 4\sqrt{3}=2\sqrt{3}$

Answer:

$2\sqrt{3}$ meters