How to find distance between center of rectangle and bound with degree?

Question

Given width and height of rectangle, coordinates of centroid and degree, how to find coordinates of a point extended from centroid with degree?
In the below image, I want to calculate (??, ??). Any advise will be appreciated. Thanks in advance.

Answer 1

We can assume $x_1 = y_1 = 0$, if you need another point then just shift all numbers by $x_1$ and $y_1$.

It's easy to use trigonometry to show that the point where the line intersects the right edge (or its extension) will be $\left(x_3, \frac{y_3}{\cos \theta}\right)$. You can compute the other ones too, for example the top edge will meet at $\left(\frac{x_2}{\sin \theta}, y_2\right)$.

Now just use a simple approach, the Pythagorean theorem, to see which point is the first point that the line intersects.