QuestionIn $\triangle A B C, m \angle A=60^{\circ}, m \angle C=30^{\circ}$, and $A B=6$ inches. What is the length of side $B C$ ? A. 5.19 inches B. 8.48 inches C. 10.39 inches D. 12 inches

Studdy Solution
Solve for $BC$:
$$BC \cdot \frac{2}{\sqrt{3}} = 6 \cdot 2$$
$$BC \cdot \frac{2}{\sqrt{3}} = 12$$
$$BC = 12 \cdot \frac{\sqrt{3}}{2}$$
$$BC = 6\sqrt{3}$$
Calculate $6\sqrt{3}$ using an approximation for $\sqrt{3} \approx 1.732$:
$$BC \approx 6 \times 1.732$$
$$BC \approx 10.392$$
The length of side $BC$ is approximately $10.39$ inches, which corresponds to option C.