Ambiguous case using law of sines
Hello, here is the data I am given to work with:
Angle A=30 deg
So I know that I can take the 3/sin30 = 4/sinC
Rearranging that, I am left with SinC = Sin(30)(4)/3 which can further be simplified to 41.81 deg.
So does having two acute angles (30 deg. and 41.81 deg) account for the fact that it is ambiguous? Since we do not know the obtuse angle in the first place, which enables us to that think when we find out that angle C is acute, and we already have an acute angle, there is the possibility that it could actually be obtuse?
Also, I do not understand this part of the explanation in the book to this problem:
"Since angle C lies in a triangle a=30 deg. we must have that C greater than 0, but less than 150. There are two angles of C that fall in this range and have SinC = 2/3: C = (2/3) radians approx. 41.81 deg. and c = pi - arcsin (2/3) radians approx. 138.19 deg.
So I can comprehend the first sentence, but in the rest of the sentences I do not understand why they throw in pi and radians. I know pi is equal to 180 deg., but why did they throw in pi and radians so suddenly?