Answer
$82.5^{\circ}$
Work Step by Step
We found in part (a) that x component of $\vec{r} $ is $1.59\,m$ and in part (b) that y component of it is equal to $12.07\,m$.
Let $\theta$ be the angle $\vec{r}$ makes with the positive direction of x-axis.
Then,
$\tan\theta=\frac{opposite\,side}{adjacent\,side}=\frac{y\,component}{x\,component}=\frac{12.07\,m}{1.59\,m}$
Or $\theta= \tan^{-1}(\frac{12.07}{1.59})=82.5^{\circ} $
