How do you determine whether #triangle ABC# has no, one, or two solutions given #A=44^circ, a=14, b=19#?

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Answer 1 · 2017-07-10T17:43:18

Compute the height of the triangle:

#h = bsin(A)#

#h = 19sin(44^@)#

#h ~~ 13.2#

We have the situation were #h < a < b#:

#13.2 < 14 < 19#

As you can see from the reference for the The Law of Sines -Ambiguous Case, this means that there are 2 possible triangles.