SOLUTION: Solve the triangle. A = 46°, a = 34, b = 27 I know that B = 34.8°, C = 99.2° but can't figure what c is. Is this triangle solvable?

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the triangle. A = 46°, a = 34, b = 27 I know that B = 34.8°, C = 99.2° but can't figure what c is. Is this triangle solvable?       Log On


   

Question 982564: Solve the triangle.
A = 46°, a = 34, b = 27
I know that B = 34.8°, C = 99.2° but can't figure what c is. Is this triangle solvable?
Found 2 solutions by macston, rothauserc:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
Law of Sines:
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a%2F%28sinA%29=c%2F%28sinC%29
c=%28a%2AsinC%29%2F%28sinA%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we use the law of sines, that is
(a/sin(A)) = (b/sin(B)) = (c/sin(C))
we are given
(34/sin(46)) = (27/sin(B))
34sin(B) = 26sin(46)
34sin(B) = 18.702834809
sin(B) = 0.550083377
note use inverse sin function to find angle B
B = 33.372733167 approx 33.4 degrees then
C = 180 - (46 + 33.4) = 100.6
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(b/sin(B)) = (c/sin(C))
27/0.550083377 = c/0.982935349
0.550083377 * c = 27 * 0.982935349
0.550083377 * c = 26.539254427
c = 48.245876056 approx 48.2
therefore
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A=46 degrees, B=33.4 degrees, C=100.6 degrees
a=34, b=27, c=48.2
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