The above diagram shows this situation. We have to find the values of x and y
Definition of sine
[tex]\sin (angle)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]Applying this definition to the angle of 50°, and solving for x:
[tex]\begin{gathered} \sin (50^o^{})=\frac{x}{200} \\ \sin (50^o)\cdot200=x \\ 153.21\approx x \end{gathered}[/tex]Definition of cosine
[tex]\cos (angle)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]Applying this definition to the angle of 50°, and solving for y:
[tex]\begin{gathered} \cos (50^o)=\frac{y}{200} \\ \cos (50^o)\cdot200=y \\ 128.56\approx y \end{gathered}[/tex]Answer: The car traveled 153.21 miles east and 128.56 miles north
