because sin(69.5) = sin(110.5) ... the cosine law has no ambiguity.
What doesn't the two always work? For example, 1) Find the magnitude of the resultant vector of forces 117N and 223N acting at an angle of 140^o to one another. Find the angle between the resultant and the 117N force.
The resultant force is 153.1N and the angle between the force and with the 117N force with the sine law is 69.4^o. But with the cosine law it is 110.5^o. Why does this happen? My teacher doesn't know why they give two different answers, and the entire class, but one, got the angle with the sine law and thought, along with the teacher, that the 69.4^o was correct. However, knowing that the size of the angle and the length of the sides opposite of the angles increase/decrease proportionally. This means the 69.4^o answer is wrong because it is second largest angle opposite to the largest side of the triangle, therefore proving that the 110.5^o is correct!