Question

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

Answer 1

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:

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^@`