I have a problem of Height and Distance.Plz check it !!!!!!!

A spherical ball of radius 'r' placed on the ground subtends an angle of 600 at point A of the ground. What is the distance between the center of the ball and the point A?

In an equilateral triangle all three sides are of the same length and let this be 'a' units.

From the diagram it is clear that OA is the angle bisector of angle LAM.

Therefore, angle OAL = 30
In the right triangle OAL, sin 30 =
We know that OL is the radius of the sphere = r
Therefore,
Or

OA = 2r