Determine if it is one triangle, two triangles, or no triangles given the information

Question

b=4, c=6, B=20 (my book answer says two triangles but I have no idea how they did the problem to figure it out)

Answer 1

If B is an angle of 20 degrees and c and b are sides, then the easiest way to get the answer is to graph this information on DESMOS, which will make it clear the book answer is correct.

Otherwise use the Law of Sines to compute angle C

Then get angle A by subtraction of B and C from 180.

Then the either the Law of Sines or the Law of Cosines will get you length a.

Answer 2

Here is a Desmos graph modelling Law of Sines Ambiguous Case. In this graph A and a are used for the angle and side opposite. Lower case "c" is the other given side. Click the rows labelled "highlight obtuse triangle" and "highlight acute triangle" to see the two triangles that are possible.

desmos.com/calculator/bey9nrm70w