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:

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