Trigonometry problem

Points (a,b) (c,d) and (e,f) are points on a map


I want to calculate the co-ordinates of point (a,b)

s1 and s2 are known length (about 3 miles)

Co-ordinates of (c,d) and (e,f) are known


All co-ordinates are in dd mm.mmm format which may make things slightly harder.

Can anyone devise a pair of simultaneous equations to find a and b?

I know roughly what the (a,b) are for my values of c,d,e,f,s1 and s2 because I've plotted them on a map

some questions:
-1- What kind of earth projection are you using?(A straight line on one map is a curved on a another!). Or do you consider the distances as so small, that no earth projection is to be considered (that would be the easiest one)!
-2- You are you looking for one point, but there could be two points matching the data (2 circles intersecting!)
-3- The distance given is in miles (statute or nautical)?

Looking for one point as I know the unknown point is north of the other two
Statute miles


I've found a solution now anyway

Thanks :)