How do you determine whether $△ A B C$ $triangle ABC$ has no, one, or two solutions given $A = 44^{\circ}, a = 14, b = 19$ $A=44^circ, a=14, b=19$ ?

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Answer 1 · 2017-07-10T17:43:18

Compute the height of the triangle:

$h = b sin (A)$ $h = bsin(A)$

$h = 19 sin (44^{\circ})$ $h = 19sin(44^@)$

$h \approx 13.2$ $h ~~ 13.2$

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

$13.2 < 14 < 19$ $13.2 < 14 < 19$

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

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