Question

Solve the triangle. A=32 degrees, a=19, b=14

Answer 1

what's there to "solve"?

Answer 2

Sides B and C and angle c

Answer 3

are you doing trig I assume? have you done the Law of Sines yet?

Answer 4

That's what we are doing now

Answer 5

ok, then

Answer 6

$$
\cfrac{sin(B)}{14}=\cfrac{sin(32)}{19}\implies sin(B) =\cfrac{14sin(32)}{19}
$$

Answer 7

solve for angle B using law of sines
\[\frac{\sin B}{14} = \frac{\sin 32}{19}\]
from there you get angle C
\[C = 180 - 32-B\]
then solve for side c using law of sines again
\[\frac{c}{\sin C} = \frac{19}{\sin 32}\]

Answer 8

so, the rational above, as dumbcow showed, will give you a number, then arccosine bothe sides to get the angle B
and the angle C will be
180-(A+B)

Answer 9

as as dumbcow showed above, use the Law of Sines, once you have the angle C, to get the side "c" :)