This is my first post here so please bear with me as this is probably a well known problem with an easy solution that I most likely should know at age 28, however, seeing as how I don't, I thought I would try asking people who are smarter than me for help. I am trying to figure this one out without a long formula. Probably doesn't exist, but need an expert's and an experienced mathmatician's help first of all, to show me the standard formula in solving this problem as well as (if any) some tips and tricks or "unorthodox" so to speak ways in solving it.

So, Dude and I, the two observers, are standing 1 mile apart from each other.

We both see in the distance a really tall building. On the very top of this building there is a huge Radome antenna.

Neither of us know

the height of the building nor do we know the size of Radome on top of the building.

Using an astrolabe, we find the degrees of altitude of the Radome from both standpoints.

Mine shows the Radome at 60° altitude and Dude's astrolabe shows 70° altitude.

With these factors being the only measurements we have (we don't know the size of the radome, height of building)

what is the mathematical formula(s) or

equation(s) to find both the

size of the Radome as well as how high off the ground it is.

(The building in this problem is technically irrelevant considering we don't know the height of it)

Again, I'm probably going to get some responses saying this is so easy a 5th grader could figure it out, basically, if not saying it bluntly, that I'm a moron. But I realize this going into it and my whole goal in asking this question is to learn how to solve the problem because I don't know how. Or I just don't remember what my teacher taught me over 10 years ago. Please refresh my memory or teach me the right way and hopefully some short cut way as well. Thanks!2234

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