Answer
$v\approx\left\langle 16.712,19.917 \right\rangle$
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 $|v|=26$ and $\theta=50^{\circ}$ therefore,
the horizontal component is
\begin{align*}
a=&|v|\cos\theta\\
a=&26\cos50^{\circ}~~~ \text{use} ~~\theta=50^{\circ} ,|v|=26\\
a=&26\times 0.642788\\
a=&16.712 ~~~(\text{approximated to three decimal places}),
\end{align*}
and the vertical component is
\begin{align*}
b=&|v|\sin\theta\\
b=&26\sin50^{\circ}~~~ \text{use} ~~\theta=50^{\circ} ,|v|=26\\
b=&26\times 0.766\\
b=&19.917 ~~~(\text{approximated to three decimal places}).
\end{align*}
Hence, the vector $v=\left\langle a,b \right\rangle\approx\left\langle 16.712,19.917 \right\rangle$ .
