The Round Earth

Project #1

Assume that x is the height the tallest mast on a sail boat. Create a table of mast heights (10, 20, 30, 40, ..., 100) and how far a boat must sail (longitude/degrees) before the top of the mast is no longer visible.

Display the angle in degrees, minutes, seconds.

Project #2

Add to the table created in Project #1 how far the boat has sailed in feet, miles, nautical miles, meters, and/or kilometers.
Remember distance traveled is on the surface of the earth which is curved.

Project Assumptions and Equations

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rradius of the earth
adjacent side of right triangle and angle θ
xheight of mast
r + xhypotenuse of right triangle
θangle
(at the equator it is a measure of east/west longitude)

Note: θ is an acute angles that is greater than 0° and less than 90°

import numpy as np hypotenuse = r+x = r/np.cos(θ) θ = np.arccos(r/(r+x))
Notes:
1. If (y/h) is the cosine of θ, then θ is the arc cosine of (y/h).
2. In Python the angles are measured in radians, not degrees.
45 deg = 0.7854 rad 90 deg = 1.5708 rad 135 deg = 2.3562 rad 180 deg = 3.1416 rad

What is Sine and Cosine

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