Question

Consider a triangle ABC like the one below. Suppose that A = 27°, C = 78°, and b = 66. (The figure is not drawn to scale.) Solve

Answer 1

We don't get to see the figure but we don't need it.

The remaining angle B is

B = 180 - 27 - 78 = 75°

The Law of Sines gives the remaining sides

$\dfrac{a}{\sin A} =\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

$a = \dfrac{b \sin A}{\sin B} = \dfrac{66 \sin 27}{sin 75} \approx 31.0203$

$c = \dfrac{b \sin C}{\sin B} = \dfrac{66 \sin 78}{sin 75} \approx 66.8350$

Answer: B=75°, a=31.0, c=66.8

No need for "or" on this one.  That happens when we know the sine of an angle so there are two possibilities for the angle, an acute one and an obtuse one that's supplementary.