In triangle ABC, a=12.2, B=14.0, <A=43°, how do you find <B?

1 Answer
Alan P.
Jun 2, 2015

Given a triangle ABC with
#color(white)("XXXXX")##/_A = 43^@#
#color(white)("XXXXX")##a=12.2#
#color(white)("XXXXX")##b=14.0#

We can use the Law of Sines
#color(white)("XXXXX")##(sin(A))/a = (sin(B))/b#

to determine a solution for #/_B#
#color(white)("XXXXX")##/_B = arcsin((b*sin(A))/a) = 51.5^@#

BUT there are two possible solutions
#color(white)("XXXXX")#as indicated in the diagram below:
enter image source here

The angle given by the Law of Sines is actually the angle for #/_B_2# in the diagram

#/_B_1 = 180^@ - 51.5^@ = 128.5^@#

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