Given triangle ABC with $A=30°$, $B=45°$, and side $a=10$, use the Law of Sines to find the length of side $b$.

• A. $b=\frac{10\cdot sin(30°)}{sin(45°)}=7.07$
• B. $b=\frac{10\cdot sin(45°)}{sin(30°)}=14.14$
• C. $b=10$
• D. $b=5$

Answer: (B)

Verified step by step guidance

1. Identify the given elements in triangle ABC: angle A = 30°, angle B = 45°, and side a = 10 (opposite angle A). We need to find side b, which is opposite angle B.
2. Recall the Law of Sines formula: \(\frac{a}{\sin A} = \frac{b}{\sin B}\). This relates the sides of a triangle to the sines of their opposite angles.
3. Rearrange the Law of Sines to solve for side b: \(b = a \times \frac{\sin B}{\sin A}\).
4. Substitute the known values into the formula: \(b = 10 \times \frac{\sin 45^\circ}{\sin 30^\circ}\).
5. Calculate the sine values for 45° and 30° (using known exact values or a calculator) and then multiply and divide accordingly to find the length of side b.