1. The problem is to simplify the expression $$Vi \sin 30 \times \frac{171}{Vi \cos 30}$$. 2. Recall the trigonometric values: $$\sin 30 = \frac{1}{2}$$ and $$\cos 30 = \frac{\sqrt{3}}{2}$$. 3. Substitute these values into the expression: $$Vi \times \frac{1}{2} \times \frac{171}{Vi \times \frac{\sqrt{3}}{2}}$$ 4. Simplify the expression by canceling $$Vi$$: $$\cancel{Vi} \times \frac{1}{2} \times \frac{171}{\cancel{Vi} \times \frac{\sqrt{3}}{2}} = \frac{1}{2} \times \frac{171}{\frac{\sqrt{3}}{2}}$$ 5. Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{1}{2} \times 171 \times \frac{2}{\sqrt{3}}$$ 6. Simplify the multiplication: $$\frac{1}{2} \times 171 \times \frac{2}{\sqrt{3}} = 171 \times \frac{1}{\sqrt{3}}$$ 7. Rationalize the denominator: $$171 \times \frac{1}{\sqrt{3}} = 171 \times \frac{\sqrt{3}}{3} = \frac{171 \sqrt{3}}{3}$$ 8. Simplify the fraction: $$\frac{171 \sqrt{3}}{3} = 57 \sqrt{3}$$ Final answer: $$57 \sqrt{3}$$