Use the Law of Sines to find the angle $B$ to the nearest tenth of a degree.

• A. 48.6°
• B. 77.2°
• C. 40.5°
• D. 35.3°

Answer: (A)

Verified step by step guidance

1. Identify the given values in the triangle: side a = 4, side b = 6, side c = 7.8, and angle C = 30°.
2. Recall the Law of Sines formula: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \).
3. Use the Law of Sines to set up the equation for angle B: \( \frac{b}{\sin B} = \frac{c}{\sin C} \). Substitute the known values: \( \frac{6}{\sin B} = \frac{7.8}{\sin 30°} \).
4. Calculate \( \sin 30° \), which is 0.5, and substitute it into the equation: \( \frac{6}{\sin B} = \frac{7.8}{0.5} \).
5. Solve for \( \sin B \) by cross-multiplying and simplifying: \( \sin B = \frac{6 \times 0.5}{7.8} \). Then, use the inverse sine function to find angle B to the nearest tenth of a degree.