Mountain Vertex
How do I find the angle formed at the center of the earth using given data?
A person is standing on the shores of Oahu looking straight at a mountain so that line of sight is tangent to the surface of the earth. A right triangle is formed by person's line of sight, radius from center of earth to point at which person is standing, and line from center of earth through mountain (note peak of the mountain is NOT a vertex of the triangle). The radius of the Earth is 3960 miles and for the mountain, the distance from Oahu is 65 miles and the height is 3,370 feet.
Any help would be appreciated!
Since I posted my original answer to this question, I have had a sleep, and it has become clear that this question is not really concerned with distance on the surface of the Earth, and tangents and so on, but simply about right triangles.
There is a right angle at the observers position. There is a short leg of 65 miles, and a long leg of 3960 miles, and you want the angle opposite the short leg of the triangle.
The tangent of this angle = 65 / 3960 = 0.016414
So the angle is tanˉ¹ 0.016414 = 0.94º
And that's it. All the stuff about mountains, line-of-sight and so on is unnecessary verbiage.
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