Sun position at sunrise & sunset

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There are many many references telling me what time the sun will rise and set. There are also references telling me the sun's latitude on a given day.

But...

I want to find out where the sun will touch the horizon from where I'm standing. For instance, right now I'm at a latitude of 38.6799437 N. And the sun is at a latitude of 4.2333333 S.

Now, going off of memory from this morning, the sun came up around a heading of 107°. I want to find out exactly where based on my and the sun's position, which can both vary.

I'm thinking that this is spherical math, but that's more than I ever took. I also realize that mountains and buildings will affect the answer a bit, so we'll have to assume a clear site to the horizon.

Thanks