1. The problem is to evaluate the expression $$BC = 18.4 \times \frac{\sin 58^\circ}{\sin 50^\circ}$$ given the formula. 2. This formula likely comes from the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$. 3. Here, $18.4$ is a side length opposite to an angle of $50^\circ$, and we want to find side $BC$ opposite to $58^\circ$. 4. Substitute the values into the formula: $$BC = 18.4 \times \frac{\sin 58^\circ}{\sin 50^\circ}$$ 5. Calculate the sine values: $$\sin 58^\circ \approx 0.8480$$ $$\sin 50^\circ \approx 0.7660$$ 6. Substitute these values: $$BC = 18.4 \times \frac{0.8480}{0.7660}$$ 7. Simplify the fraction: $$\frac{0.8480}{0.7660} \approx 1.1077$$ 8. Multiply: $$BC = 18.4 \times 1.1077 \approx 20.37$$ 9. Therefore, the length $BC$ is approximately $20.37$ units.