distance earth math

[Jurgen.v26]

the earth has a radius of 6371km
I am standing on a 2,820km mountain and take a picture where mountain is seen 443km away, this mountain is 4,102km high.
There is only sea between these 2 mountains.
The Bulging of the earth for 443km is around 15,4km
How can I mathematically prove this is possible, taking in account the earth curve?

 

[Deleted member 4993]

the earth has a radius of 6371km
I am standing on a 2820m mountain and take a picture where mountain is seen 443km away, this mountain is 4102m high.
There is only sea between these 2 mountains.
How can I mathematically prove this is possible, taking in account the earth curve?

If I were to do this problem, I would draw an approximate sketch of the situation, and see graphically what do I need to prove.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[Dr.Peterson]

Your calculation of the "bulge" agrees with mine. But I don't think it's directly usable to answer your question.

I used a formula for the distance to the horizon, and found it is 189.6 km and 228.7 km for the two mountains, respectively, so that one could be barely seen from the other at 189.6 + 228.7 = 418.3 km apart. If they are farther, then this model says they couldn't see each other. But it's close.

It could be that the effective radius is different from what you used, or there is some other inaccuracy in your modeling. (I don't see any pair of mountains in Wikipedia that fit your description ...)