Suppose A and B represent two vectors (insame order), the angle between them being 60 degrees, then why is the resultant wrong?

Question

Let's say there are three points A,B and C:
A represents the displacement between points A and B (4 cm to the east) and B represents the displacement between the points B and C (3cm to the northwest).And the angle formed ( anglevCBA) is 60 degrees.

The (magnitude of) resultant vector C would be:

So, according to the triangle law of addition , the answer should be:$\sqrt{37}$ or 6.08
I made a diagram (with some precision), which looked something like:

On actual construction, I found the magnitude of the resultant to be 3.62 (maybe it was 3.65 cm. Somewhere between 3.60 and 3.70. The point is, it wasn't 6.08 cm.- {Quite far from it}).
The question is/are:

• What did I do wrong?
• Is there something wrong with my interpretation of vector addition?
• And the important question: How do we show this triangle addition law visually? (since, this doesn't seem correct )
  
  

// Didn't see any 'beginner' tag in the search result while posting this question

Answer 1

You’re adding $\vec{A}$ and $\vec{B}$, and your formula is correct as long as you take $\theta$ to be the angle between them, which is 120 degrees, not 60. Pay attention to the direction of the vectors.

Answer 2

I would say you misplaced a $+$ where it should be a $-$: $$ c^2=a^2+b^2-2\,a\,b\,\cos\gamma $$ With this, we get a length of $c=3.61\text{ cm.}$