If we have the angle and magnitude of a vector A we can find its Cartesian components using the following formula
[tex]A_x = |A|cos(\alpha)\\\\A_y = |A|sin(\alpha)[/tex]
Where | A | is the magnitude of the vector and [tex]\alpha[/tex] is the angle that it forms with the x axis in the opposite direction to the hands of the clock.
In this problem we know the value of Ax and Ay and we need the angle [tex]\alpha[/tex].
Vector A is in the 4th quadrant
So:
[tex]A_x = 6\\\\A_y = -6.5[/tex]
So:
[tex]|A| = \sqrt{6^2 + (-6.5)^2}\\\\|A| = 8.846[/tex]
So:
[tex]Ay = -6.5 = 8.846cos(\alpha)\\\\sin(\alpha) = \frac{-6.5}{8.846}\\\\sin(\alpha) = -0.7348\\\\\alpha = sin^{- 1}(- 0.7348)[/tex]
[tex]\alpha[/tex] = -47.28 ° +360° = 313 °
[tex]\alpha[/tex] = 313 °
Option 4.
