Observe the figure :

Let be the distance from the center of the green to the marker position which is .

be the distance from the center of the green to the ball position.

be the distance from  the marker position to the ball position which is .

Now find the side .

Apply cosines law : .

Substiute ,  and .

Therefore, the distance from the center of the green to the ball position is .

Distance from the center of the green to the ball position is .