How do you use the law of sines to solve the triangle given A = 165.1°, B = 81.9°, b = 18.6?

1 Answer
May 28, 2015

The law of sines says that in a triangle where the angle alpha is opposite the side of length a, angle beta - length b and angle gamma - length c and R is the radius of the circumscribed circle (the smallest circle possible that contains the triangle / passes through all three vertices) we have the following:
a/sin alpha = b/sin beta = c/sin gamma = 2R
and you can use any two of these, e.g. b/sin beta=2R.

In your question values A and B are given in degrees so one can assume that they're the angles alpha and beta but their sum is 247^@ which is a little bit too much since in all triangles the sum of all three angles is always 180^@. Please check where the mistake in those values is :)