The horizontal Force $A_x$ is easy but how did they get the vertical forces $A_y$ & $B_y$? I tried using similar triangles for the Force and length of the sides, somehow I can't manage to solve it. I wonder where I am making a mistake.
There are multiple ways to solve this problem but I use the moment equilibrium around the points A and B.
$$A_y 3l-q_0 4l^2=0$$
You can find the $A_y$ reaction force from the equation above and use it again in the moment equilibrium around A this time:
You can also skip the second part, and use your intuition, since the structure is in equilibrium, the vertical forces should cancel each other out, otherwise the structure accelerates.