lower left coordinates should be $\displaystyle (-20,-200)$
angle between the segment A and the y-axis ...
$\displaystyle \theta = \arctan\left(\frac{1}{10}\right)$
angle between the segment in quad I and the x-axis = $\displaystyle 120 - \left[90 + \theta \right] = 30 - \theta$
$\displaystyle |A| = \sqrt{20^2 + 200^2}$
$\displaystyle x = |A|\cdot \cos(30-\theta)$
$\displaystyle y = |A| \cdot \sin(30 - \theta)$