# Height of an island beyond the horizon

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1. Nov 21, 2017

### fizixfan

You said, “Normally, wouldn't you measure the distance from the observer to the island by the distance (arc length) along the surface between them?”

2. Nov 21, 2017

### fizixfan

I’m measuring the distance by line of sight, not by the distance along the surface. How far you can see is not the same as arc length - it’s a straight line.

3. Nov 21, 2017

### LCKurtz

I understand how you are measuring the distance. It's your problem and you can do it any way you wish. I am just pointing out that the standard way to measure the distance between two points on earth is along an arc on the surface between them. If the earth were a perfect sphere these arcs would be on great circles. And, as you have noticed, for your particular calculation it doesn't make much difference.

4. Nov 22, 2017

### fizixfan

Fair enough. My apologies if I insulted you - it was uncalled for.

As for this (from post #19):

"Calculate d and s in terms of the angle α and radius r. Can you see why d>s?"

No, I tried but I can't see it. I could only prove it in one case (post #16), i.e., for α = 45°. I'm too old and rusty to do a general proof.

Thanks for your help though - I appreciate it.