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

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

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)((10*0.669130606359)/(16))`

`B=\text{sin}^(-1)((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.