java - Elevation Angle between Positions -

i'm using java nasa worldwind, , have 2 objects different elevations , positions.

how can find elevation angle between objects taking account curvature of earth?

this image illustrates (obviously not scale) i'm trying do:

object 50 feet above ground, , object b 500 feet above ground. how can find angle x, taking account curvature of earth?

trigonometry saves day! please refer untidy diagram work through answer:

the angle want find α. can find θ if know distance (along curvature of earth) between 2 points (or more accurately, curved-line distance between 2 points on surface on earth, if extend line each object down surface). if distance l, θ l/r (see arc length) r radius of earth.

notice values d₁, d₂, , d₃. can find α if know d₂ , d₃, because (θ + α) inverse tangent of d₂/d₃. how find these?

first we'll find d₁. know hypotenuse of triangle d₁ , d₃ r + h_a, radius of earth plus elevation of object a. hence can find d₁:

similarly, d₃:

now how find d₂? know total length of base of entire triangle r + h_b; radius of earth plus height of object b. know d₁. d₂ is:

now ready find α:

so using expression in terms of heights of both objects , radius of earth, should able find α. there may easier way find α, able come with; it's been while since did trigonometry! think math correct, let me know if spot wrong.