SOLUTION: in triangle ABC,a=7.8, b=4.2, c=3.9. find B to the nearest tenth. a)15.1 degrees b)148.7 degrees c)78.9 degrees d)16.2 degrees

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: in triangle ABC,a=7.8, b=4.2, c=3.9. find B to the nearest tenth. a)15.1 degrees b)148.7 degrees c)78.9 degrees d)16.2 degrees      Log On

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Question 211795: in triangle ABC,a=7.8, b=4.2, c=3.9. find B to the nearest tenth.
a)15.1 degrees
b)148.7 degrees
c)78.9 degrees
d)16.2 degrees
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
We use cosine law to solve this problem:
b%5E2=a%5E2+%2B+c%5E2+-2ac%2Acos+B
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Solving for cos B,
cos+B=%28a%5E2+%2B+c%5E2+-+b%5E2%29%2F%282ac%29%0D%0A++++++++=%287.8%5E2+%2B+3.9%5E2+-+4.2%5E2%29%2F%282%2A7.8%2A3.9%29=0.9601
B=arc cos 0.9601=16.2 degrees