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 :)