Answer
$869,418$
Work Step by Step
Converting angle to decimal degrees:
$154^{\circ}20'=154\frac{20}{60}=154.33^{\circ}$
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 $|\textbf{v}|=964$ and $\theta=154.33^{\circ}$ in the formulas above,
$x=964\cos154.33^{\circ}\approx-869$
$y=964\sin154.33^{\circ}\approx418$
Therefore, $|\textbf{v}|=\langle -869,418 \rangle$
Since the question requires magnitudes of horizontal and vertical components, the magnitude of horizontal component is $869$ and the magnitude of vertical component is $418$.
