Question : Adding horizontal & vertical feet onto a latitude/longitude waypoint?

In the below diagram I have two points, P0 and P1.  I am trying to find the latitude and longitude of P3.  

The center of P0 is at 34.1837710, -118.9484950 and the center of P1 is at 34.1946740,-118.9249500.

I know that "r0" is 7764 feet and "r1" is 3574 feet so using the formulas at the link below, I found that the length of "a" is 6987.7 feet and "h" is 3384.0 feet.

But now mathematically, how to I get the latitude and longitude of P3?

http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/

Answer : Adding horizontal & vertical feet onto a latitude/longitude waypoint?

Great question - lots of stuff in the literature for going the other way into the formula.  One of the keywords is "Haversine" - that matters if you traverse substantial distances but you can probably get away with plane geometry if the distances are like what you have shown in the example.

Not a solution, but good reading here:
http://www.movable-type.co.uk/scripts/latlong.html

Just a thought, if you don't get the answer you need in these zones, ask a moderator to add this to the "Algorithms" Zone.  It seems to have a bunch of academic types that look at questions over there.

Best regards, ~Ray