The curvature of Earth and topography determine the distance to the visible hori

Question

The curvature of Earth and topography determine the distance to the visible horizon. Imagine you are standing at sea level and looking at the horizon on a clear day with no obstructions and that you can barely see the peak of a mountain you know has an elevation of the peak of 2, 500 m. How far away is the peak of the mountain? You can assume Earth is a sphere with radius of 6, 371 km. What error results on a 150 ft sight with a level if the rod reading is 10.21 ft, but the top of the 16 ft rod is 1 foot out of plumb?

Explanation / Answer

Assume that earth is perfectly sphere with radius 6371 km and as given in question that observation point is at MSL. then the distance of mountain having height of peak 2500m is

178.6 km

Calculations: Form a triangle with assuming the centre of the earth O as first point, the horizon point (A) is at right angle and the Peak of hill (B) as the third corner.

Simply by applying Pythagoras's theorem, we can get the answer.

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