How do you solve the triangle ABC, given a=15, A=94, b=12?

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Answer 1 · 2017-01-04T04:13:18

Angle A is obtuse, therefore, the ambiguous case does not apply and there is only one possible triangle. Use the Law of Sines to solve.

#sin(A)/a = sin(B)/b = sin(C)/c#

#B = sin^-1(b/asin(A))#

#B = sin^-1(12/15sin(94^@))#

#B ~~ 52.9^@#

#C ~~ 180^@ - 94^@ - 52.9^@#

#C ~~ 33.1^@#

#c = asin(C)/sin(A)#

#c ~~ 8.2#

The solution for the triangle is:

#a = 15, b = 12, c ~~ 8.2, A = 94^@, B ~~ 52.9^@, and C ~~ 33.1^@#