Finding the sum vector given only the moduli and angle

[K.QMUL]

Homework Statement

Given two 2-dimensional vectors $\overline{a}$ and $\overline{b}$ of moduli l$\overline{a}$l = 3u and l$\overline{b}$l = 4u, and forming an
angle  of 120 degrees between them, determine the modulus of the sum vector $\overline{s}$ = $\overline{a}$ + $\overline{b}$
and the angle between $\overline{s}$ and $\overline{a}$.

Homework Equations

a.b = l$\overline{a}$ll$\overline{b}$lcosθ

The Attempt at a Solution

All if have calculated is the dot product of vectors a and b, coming to (6u²). I cannot seem to figure out what I can do to find the sum of these vectors only given the moduli and angle between them. Please Help :-)

 

[K.QMUL]

I think I have solved my own question. I think I have to use the cosine rule and not the vector product rule as stated above

 

[SammyS]

I think I have solved my own question. I think I have to use the cosine rule and not the vector product rule as stated above

What do you get for your answers?