Use the Law of Cosines to Solve the ambiguous case.?

Question

Use the Law of Cosines to Solve the ambiguous case.
α = 30.0°
a = 4.53
b = 9.06

please click on the link below to see the actual problem. Thank you so much for helping me.
http://www.fbixtreme.com/17.jpg

Answer 1

I assume that 30 deg is the included angle between the legs given.

Then c^2 = a^2+b^2 -2abcos 30

plug and chug:
c^2= 31.518
c= 5.614

Why is this called the ambiguous case? I'd recommend making a sketch to see if this makes sense. Btw, cos 30 comes from a 1, sqrt(3), 2 right triangle. cos 30 is sqrt(3)/2 = 0.866

Answer 2

Ya, just solve for the third side using the cosine law,, 30 being angle between a & b...
Since this is not, and CANNOT, be a right triangle, any solution is OK..