Question 149727: Should the triangle be solved beginning with Law of Sines or Law of cosines. Then solve the triangle and round to the nearest tenth. a=16,b=13,c=10
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! To completely solve a triangle, you have to know 3 elements, either sides or angles. If it's 3 angles, then you cannot determine the sides, only the ratios of the sides.
If you have 3 sides, as in this case, use the cosine law to find one angle. Then use the law of sines to find the other angles. You can use the cosine law for all 3, but the sines is simpler once the 1st angle is known.
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Then solve the triangle and round to the nearest tenth. a=16,b=13,c=10
Pick any angle:
100 = 425-416*cos(C)
cos(C) = 325/416 = 0.78125
C = 38.625 degrees
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a/sin(A) = b/sin(B) = c/sin(C) = 10/0.62422 = 16.02
So sin (A) = a/16.02 = 0.99875
A = 87.13 degs
do B as a check:
sin(B) = b/16.02 = 0.81148
B = 54.24 degs
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Check A+B+C = 180
They add up to 179.996, within roundoff error.
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