Question

In triangle ABC, BC = a = 16, AC = b = 10, and m angle A = 42°. Which equation can you use to find m angle B?

Answer 1

c2 = a2 + b2 − 2ab cos C = 162 + 102 − 2(10)(16) cos 22°

Answer 2

Answer:

$\frac{\text{sin(B)}}{10}=\frac{\text{sin}(42^{\circ})}{16}$

Step-by-step explanation:

Please find the attachment.

We have been given that in triangle ABC, side $BC=a=16$, side $AC=b=10$ and measure of angle A is 42 degrees. We are asked to find an equation that can be used to find the measure of angle B.

We will use law of sines to solve our given problem.

$\frac{\text{sin(A)}}{a}=\frac{\text{sin(B)}}{b}=\frac{\text{sin(C)}}{c}$

Upon substituting our given values, we will get:

$\frac{\text{sin}(42^{\circ})}{16}=\frac{\text{sin(B)}}{10}$

Switch sides:

$\frac{\text{sin(B)}}{10}=\frac{\text{sin}(42^{\circ})}{16}$

$\frac{\text{sin(B)}}{10}*10=\frac{10*\text{sin}(42^{\circ})}{16}$

$\text{sin(B)}=\frac{10*\text{sin}(42^{\circ})}{16}$

$B=\text{sin}^{-1}(\frac{10*\text{sin}(42^{\circ})}{16})$

$B=\text{sin}^{-1}(\frac{10*0.669130606359}{16})$

$B=\text{sin}^{-1}(\frac{6.69130606359}{16})$

$B=\text{sin}^{-1}0.418206628974375)$  

$B=24.72^{\circ}$  

Therefore, the equation $\frac{\text{sin(B)}}{10}=\frac{\text{sin}(42^{\circ})}{16}$ can be used to find m angle B.