Find Point P2 in Space Given Data on P1 and P2

[shininglight]

Suppose I have a point P1 on Earth's surface(in lat,long and alt). I need to locate point P2 in space(in lat,long,alt) if the following data is given.
1.Distance between P1 and P2 is 'd'
2.Altitude of P2 is 'h'
3.Bearing of P2 from P1 is theta.

Could you please help me out with the logic to solve this..Should I go for ECEF or stick on to geodetic coordinate s/m?

 

[Filip Larsen]

Seems the problem, as you quote it, is a bit underspecified.

If d and bearing is along line-of-sight vectors I would "go ECEF", that is calculate the Cartesian point of P1 and then try calculate the vector to P2 using the information given and then convert back to geographic coordinates. Note that if (east-west) distance is large it may be that bearing from P1 to P2 is not exact opposite of bearing from P2 to P1.

If distance and bearings instead are specified along great circles on the ground between the foot point of P1 and P2, I would instead try to solve it using only spherical trigonometry.