Math Is Fun Forum

Xarzu

Member

Registered: 2017-09-11

Posts: 1

Simple Law of Cosines problem

Huge suspension bridges are build with the earth's roundness in mind.  The two towers are plumb line straight up and down and yet, because of their colossal size, they are a bit further apart at their tops than they are at their base.  So, how can we calculate what this difference would be?

Here is the input data:

If we know the earth's radius; the location of the base of the towers above sea level; The distance (from the center of each base of the tower) between the bases; and the height of the tower, how would we calculate the distance from the tops of the towers.

I made this video to explain what I am talking about but I want to have the mathematical formula to predict the distance differences between the tops of the towers compared to the base:
https://www.youtube.com/watch?v=8NuNga3Bpns

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Simple Law of Cosines problem

hi Xarzu,

You've posted this as an exercise, but you've made it seem more like a help me problem.  There's a difference:  If it's an exercise, then members have a go for fun and maybe just post an answer.  If it's a help me, then much more explanation would be provided and the 'student' encouraged to do some / most of the working themselves.  Please clarify.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob