Question

what is the approximate value of b, rounded to the nearest tenth? use the law of sines to find the answer. law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ 1.9 units 4.7 units 5.0 units 5.7 units

Explanation:

Step1: Find angle C

Angle C = 180° - 66° - 76° = 38°

Step2: Apply Law of Sines

$\frac{\sin(B)}{b} = \frac{\sin(C)}{c} \implies b = \frac{c \cdot \sin(B)}{\sin(C)}$

Step3: Substitute values

$b = \frac{3 \cdot \sin(76^\circ)}{\sin(38^\circ)} \approx \frac{3 \cdot 0.9703}{0.6157} \approx 4.7$

Answer:

B. 4.7 units