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

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c2 = a2 + b2 − 2ab cos C = 162 + 102 − 2(10)(16) cos 22°
User Son Of A Beach
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8.1k points
6 votes

Answer:


\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.

In triangle ABC, BC = a = 16, AC = b = 10, and m angle A = 42°. Which equation can-example-1
User Kyle Gagnet
by
7.3k points

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