Quandaries
and Queries 

I found a geometry problem that reads as follows:In triangle ABC, <C = 3<A, side BC = 27 and side AB = 48.Find the length of of side AC. How do I solve it? I tried using the law of sin and got Sin 3X/Sin X = 48 / 27. After simplifying I get Sin^{3} X = 7/36. Am I even on the right track or is there an easier way to do this? 

Hi Jason, I agree with your method but I don't get the result that you got. You let the angle at A be X degrees and used the law of sines to produce
The expression I used for Sin (3X) is
and hence
simplifies to
Using the fact that Cos^{2}(X) = 1  Sin^{2}(X) I then get
Penny 

