To answer the question, do we need to know the length of BC?
For GMAT data sufficiency questions, we don't actually need to know how to calculate the answer. We just need to know that someone could calculate the answer based on the information provided.
In fact, the GMAT will sometimes present you with calculations that you may or may not be able to solve with the expected GMAT level knowledge (Trigonometry is above this level), but you should know whether it's possible at all. Because only 1 triangle fits that description, by using trigonometry someone could determine the length of BC.
So our thoughts here at Magoosh are, don't worry calculating the specific value. But if you love math as much as we do and are interested in understanding the principles behind it, here's a good website to check out Maths is Fun.