I'm a new Biomedical Tech student and we're working with Trigonometry of the right triangle right now and I have a problem I can't figure out: If a = x, c = 2x : find the Sine, Cosine and Tangent for angles a and b. How do you determine the value for x?

You are focusing on the wrong issue. It doesn't matter what x is. What matters is the ratio of a to c. Sin A = a/c (opp/hyp) or in your case x/2x =>1/2. To find the value of angle A simply use inverse sin of 1/2. You should be aware that sin A = cos B as they are an example of a cofunction. Once you have determined the value of angle A you can use the calculator to find each value (approximated) OR draw the triangle out & use pythagorean's theorem to find the missing side b (letting a = 1 and c= 2 remember everything is proportional) and then you will have the exact values. Obviously, if you want to work with Angle B, it is equal to 90 - Angle A or just use the cofunctions. The big idea in this problem is seeing that Sin A = 1/2.