Question

which expression represents the approximate length of bc? law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Identify knowns and unknowns

In △ABC, ∠A=66°, ∠C=38°, AB=3 (side c), find BC (side a).

Step2: Apply Law of Sines

Law of Sines: $\frac{\sin(A)}{a} = \frac{\sin(C)}{c}$

Step3: Solve for BC (a)

Rearrange: $a = \frac{c \cdot \sin(A)}{\sin(C)} = \frac{3 \cdot \sin(66^\circ)}{\sin(38^\circ)}$

Answer:

A. $\frac{(3)\sin(66^\circ)}{\sin(38^\circ)}$