Law of sine or law of cosine to solve these triangles?

Here would be a summary of how to go about it.

ASA - sine law

AAS - sine law

AAA - cannot be solved. To solve a triangle, you need at least one known side.

SSA - sine law is a better alternative. You may use cosine law, but it leads to a quadratic equation. The manipulation is much harder. You need to be careful with this, though. It leads to what we call the AMBIGUOUS CASE, where certain conditions lead you to obtaining 2 possible triangles, instead of just 1.

SAS - cosine law

SSS - cosine law

Hope this helps!!!!!

Just take a look at the two laws.

Law of Sines:
sin(A)/a = sin(B)/b = sin(C)/c

Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(A)
b^2 = a^2 + c^2 - 2bc*cos(B)
c^2 = a^2 + b^2 - 2bc*cos(C).

Just take a look at these formulas to see what variables are involved. The Law of Sines should be used when given either one side and two angles (with one of those angles being opposite to the known side) or two sides and one angle (with that angle being opposite to one of these sides) and you wish to solve for the other angle/side. The Law of Cosines should be used when given three sides (SSS) or two sides and an opposite angle. Note that AAA doesn't work with any of these laws because you cannot determine a unique triangle by just knowing the angles.

I hope this helps!