Question

find y.
image of a right triangle with a right angle, one angle 60°, one angle 30°, one leg labeled 12√6 km, the other leg labeled y
write your answer in simplest radical form.
blank kilometers

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta=30^\circ$, opposite side is $y$, hypotenuse is $12\sqrt{6}$.

Step2: Substitute values into formula

$\sin(30^\circ)=\frac{y}{12\sqrt{6}}$
We know $\sin(30^\circ)=\frac{1}{2}$, so:
$\frac{1}{2}=\frac{y}{12\sqrt{6}}$

Step3: Solve for $y$

Multiply both sides by $12\sqrt{6}$:
$y=\frac{1}{2} \times 12\sqrt{6}$
Simplify the expression:
$y=6\sqrt{6}$

Answer:

$6\sqrt{6}$ kilometers