Answer
$\theta=116^{\circ},\space or\space \theta=243^{\circ}$
Work Step by Step
Please see the attached image first.
We can write,
Vector $\vec A=cos(-35^{\circ})\space i+sin(-35^{\circ})\space j= 0.8i-0.6j$
Vector $\vec B= 1.8cos\theta\space i+1.8sin\theta\space j$
$\vec A+\vec B= (0.8+1.8cos\theta)\space i+(1.8sin\theta-0.6)\space j-(1)$
If $\vec A+\vec B$ is in y-direction, x component of the resultant vector must be zero. So, $(1)=\gt$
$0.8+1.8cos\theta=0$
$cos\theta=-\frac{0.8}{1.8}=-45$
$\theta=cos^{-1}(-45)$
$\theta=116^{\circ}\space or\space\theta=243^{\circ}$
