Question

find d.
triangle with right angle, 60° angle, 30° angle, one leg 4 mi, hypotenuse d
write your answer in simplest radical form.
blank miles

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
Here, $\theta=30^\circ$, opposite side $=4$ mi, hypotenuse $=d$.

Step2: Substitute values into ratio

$\sin(30^\circ)=\frac{4}{d}$
We know $\sin(30^\circ)=\frac{1}{2}$, so:
$\frac{1}{2}=\frac{4}{d}$

Step3: Solve for $d$

Cross-multiply: $d=4\times2$

Answer:

$8$ miles