calculate angle between two points in horizontal plane

Question

In the following figure, I have a point A at a know altitude AB from the Earth surface. For simplicity, we can assume spherical Earth. The perpendicular projection of point A to Earth surface is B (<ABC = 90 deg). Now consider another point D on Earth surface where we have connected A and D. The coordinates (latitude, longitude) for B and D are known. What is the value of angle <EAB (angle between line segments AE and AB)? Here, E is the projection of D such that <AEB = 90 deg. The figure is not to be scaled. The actual dimensions of BCED is very small compared to Earth and the figure is just for representation. Essentially AEB becomes a plane and I want to compute the angles between AE and AB with the latitude/longitude coordinates of D and B given (A has the same latitude/longitude coordinates -in degrees- as B and the altitude AB in meters is known).