Trig problem?

So this may not be the right place to post this, but I am really stumped on a math problem at the moment.

The project is to make an ISS tracker which points an arrow in the direction of the ISS, using online coordinates. I’m having some trouble finding the angle/elevation to point at, though. My thinking of how to do it is atm:

1: Find azimuth of shortest path. Calculate distance and bearing between two Latitude/Longitude points using haversine formula in JavaScript
2: Find angle of Origin>Center of the Earth> ISS location Triangle
3: input angle into triangle calculator with sides 3,959 miles and 3,959+ISSAltitude Miles

However, I am finding myself stuck at step 2, so basically I am hoping to find an equation to solve this problem: If I am here in my room at given latitude/longitude, and have a second reference point with another latitude/longitude, how can I calculate the angle of the triangle that exists between the center of the earth and those two points? (assuming a spherical earth).

For instance, if I’m at 38.897, -77.036, and trace a line to the center of the earth, and then a second line from the center to -33.856, 151.215, how can I find the angle between these two lines?

Thanks :).

Those are spherical polar coordinates and you can assume radius=1 for the purpose of calculating the angle. There are many ways, but here are a couple of suggestions: geometry - How to compute the angle between two vectors expressed in the spherical coordinates? - Mathematics Stack Exchange

However, navigating on the "celestial sphere" is just the same as on Earth, so you can use the standard routines for calculating course angle, distances, etc. but a different radius.