Answer
$v\approx\left\langle -198.004,132.052 \right\rangle$ .
Work Step by Step
The horizontal component of a vector $v=\left\langle a,b \right\rangle$ having magnitude $|v|$ and direction angle $\theta$ is given by $a=|v|\cos\theta$.
Similarly, the vertical component is given by $b=|v|\sin\theta$.
Now we have $|v|=238$ and $\theta=146.3^{\circ}$
therefore, the horizontal component is
\begin{align*}
a=&|v|\cos\theta\\
a=&238\cos146.3^{\circ}~~~ \text{use} ~~\theta=146.3^{\circ} ,|v|=238\\
a=&238\times (-0.83195)\\
a=&-198.004~~~(\text{approximated to three decimal places}),
\end{align*}
and the vertical component is
\begin{align*}
b=&|v|\sin\theta\\
b=&238\sin146.3^{\circ}~~~ \text{use} ~~\theta=146.3^{\circ} ,|v|=238\\
b=&238\times 0.55484\\
b =&132.052~~~~~~ (\text{approximated to three decimal places}).
\end{align*}
Hence, the vector $v=\left\langle a,b \right\rangle\approx\left\langle -198.004,132.052 \right\rangle$ .
