Question

find d.
write your answer in simplest radical form.
yards

Explanation:

Step1: Identify trigonometric ratio

The side length $10\sqrt{3}$ is opposite the $60^\circ$ angle, and $d$ is the hypotenuse. Use sine:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(60^\circ) = \frac{10\sqrt{3}}{d}$
We know $\sin(60^\circ) = \frac{\sqrt{3}}{2}$, so:
$\frac{\sqrt{3}}{2} = \frac{10\sqrt{3}}{d}$

Step3: Solve for $d$

Cross-multiply to isolate $d$:
$d \cdot \sqrt{3} = 2 \cdot 10\sqrt{3}$
Divide both sides by $\sqrt{3}$:
$d = \frac{20\sqrt{3}}{\sqrt{3}} = 20$

Answer:

20 yards