Calculating Angle Between Vectors Using Cosine Law

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To calculate the angle between two vectors using the cosine law, one must apply the formula c² = a² + b² - 2ab cos(C), where c is the resultant displacement and a and b are the magnitudes of the two displacements. The problem involves determining the angle that results in specific magnitudes for the resultant displacement, given two known displacements of 2.6 and 3.9. Understanding how to rearrange the cosine law formula to solve for the angle C is crucial for finding the solution. The discussion emphasizes the importance of learning the process rather than just obtaining the answer. Mastery of this concept will enhance one's ability to solve similar vector problems effectively.
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Hello, I've been trying to solve this problem for hours now, but i keep getting it wrong. Been looking for examples but i don't seem to find one with a good explanation, so any help is appreciated.

The problem:

Consider two displacements, one of magnitude 2.6 and another of magnitude 3.9. What angle between the directions of these two displacements give a resultant displacement of magnitude a) 5.7m b)2.6m c)3.2

If anyone can please help me understand, thank you. Please, don't just post the answer, i want to learn how to solve it.
 
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This is referring to addition of the displacements.

You have a triangle, and know the lengths of the 3 sides. Find the angle/s.
 
A formula that will help is the cosine law. If a triangle has sides a, b, and c and C is the angle opposite side c, then c^2= a^2+ b^2- 2ab cos(C)
 

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