Answer
$13.7,7.11$
Work Step by Step
First converting the angle to decimal degrees:
$27^{\circ}30'=27\frac{30}{60}=27.50^{\circ}$
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 $|\textbf{v}|=15.4$ and $\theta=27.50^{\circ}$ in the formulas above,
$x=15.4\cos27.50^{\circ}\approx13.7$
$y=15.4\sin27.50^{\circ}\approx7.11$
Therefore, $|\textbf{v}|=\langle 13.7,7.11 \rangle$