Answer
$38.8,28.0$
Work Step by Step
First converting the angle to decimal degrees:
$35^{\circ}50'=35\frac{50}{60}=35.83^{\circ}$
The formulas for horizontal component $x$ and vertical component $y$ of a vector $\textbf{v}$ having magnitude $|\textbf{v}|$ and direction angle $\theta$ are:
$x=|\textbf{v}|\cos\theta$ and $y=|\textbf{v}|\sin\theta$
Substituting the values of $|\textbf{v}|=47.8$ and $\theta=35.83^{\circ}$ in the formulas above,
$x=47.8\cos35.83^{\circ}\approx38.8$
$y=47.8\sin35.83^{\circ}\approx28.0$
Therefore, $|\textbf{v}|=\langle 38.8,28.0 \rangle$
