Please help ,probability question?

Question

Let S be the right-angled triangle with vertices (0,0), (1,0), (1,1). Let a be a point
chosen at randomly from within the triangle with the probability that a is in any fixed
region being proportional to the area of the region. Let T be the random variable “the angle
that the line from (0,0) to a makes with the x-axis”. Find the cdf and pdf of T.

Answer 1

I think that the statement about prob and area of regions is another way of saying that it's a joint uniform distribution:

I.e,

pdf(x,y) = 2 for x in the triangle and y in the triangle. Since the area of the triangle is 1/2 this gives P=1 for the entire triangle.

The question is: does that mean that (x,y) is uniform? I'd say yes. Now you have another problem. Since T just refers to the angle to a point a, then any line through the origin and a would have the same angle. For that reason I think that this problem is not well-posed.