In triangle $ABC$, angle $A$ is $30°$, angle $B$ is $45°$, and side $a$ (opposite angle $A$) is $10$ units. Using the Law of Sines, what is the approximate value of side $b$ (opposite angle $B$)?

• A. $14.1$
• B. $7.1$
• C. $10.0$
• D. $12.2$

Answer: (A)

Verified step by step guidance

1. Identify the given information: angle A = 30°, angle B = 45°, and side a = 10 units (opposite angle A).
2. Calculate angle C using the fact that the sum of angles in a triangle is 180°: \(C = 180^\circ - A - B\).
3. Write down the Law of Sines formula: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\).
4. Use the Law of Sines to set up the equation for side b: \(b = a \times \frac{\sin B}{\sin A}\).
5. Substitute the known values into the equation and simplify to find the approximate length of side b (do not calculate the final numeric value here).