Question

use the law of sines to find the value of a. what is the best approximation of the value of a? law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Find angle C

Sum of angles: 180° - 40° - 95° = 45°

Step2: Identify knowns

Angle A=40°, angle B=95°, side b=4.7 cm (opposite B)

Step3: Apply Law of Sines

$\frac{\sin(A)}{a} = \frac{\sin(B)}{b} \implies a = \frac{b \cdot \sin(A)}{\sin(B)}$

Step4: Calculate values

$\sin(40^\circ) \approx 0.6428$, $\sin(95^\circ) \approx 0.9962$

Step5: Compute a

$a \approx \frac{4.7 \cdot 0.6428}{0.9962} \approx 3.0$

Answer:

3.0 cm