SOLUTION: Use the law of sines to solve (if possible) the triangle. If two solutions exist, find both. 1. A=76 degrees, a=18, b=20 2. A=58 degrees, a=11.4, b=12.8

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Question 925859: Use the law of sines to solve (if possible) the triangle. If two solutions exist, find both.
1. A=76 degrees, a=18, b=20
2. A=58 degrees, a=11.4, b=12.8
Answer by Roseghanezadeh(16) (Show Source):
You can put this solution on YOUR website!
Sine rule states that: (Sin A / a) = (Sin B / b) = (Sin C / c)
1. (Sin 76 / 18) = (Sin B / 20) = (Sin C / c)
Sin B = (Sin 76 � 20) / 18 = 1.078...
B = Sin^-1 (1.078) = error
So the answer for number 1 is no solution.
2. (Sin 58 / 11.4) = (Sin B / 12.8) = (Sin C / c)
By using cross multiplication we can find the answer to B:
Sin B = (Sin 58 � 12.8) / 11.4 = 0.952...
B = Sin^-1 (0.952) = 72 degrees
now that we have two angles we can find the third angle by using this formula:
C = 180 - (A + B)
C = 180 - (58 + 72) = 50 degrees
Now we have:
(Sin 58 / 11.4) / (Sin 72 / 12.8) = (Sin 50 / c)
Now we can use cross multiplication to find c:
c = (Sin 50 � 11.4) / Sin 58 = 10.3

So these are the answers:
B = 72 degrees
C = 50 degrees
c = 10.3
And always remember to write the degree sign where it is needed.