
Index
5c. Coordinates 6. The Calendar 6a. Jewish Calendar 7.Precession 8. The Round Earth 8a. The Horizon 8b. Parallax 8c. Moon dist. (1) 8d. Moon dist. (2) 9a. Earth orbits Sun? 9b. The Planets 9c. Copernicus to Galileo 10. Kepler's Laws 10a. Scale of Solar Sys. 11a. Ellipses and First Law 
"PreTrigonometry"Section M7 describes the basic problem of trigonometry (drawing on the left): finding the distance to some faraway point C, given the directions at which C appears from the two ends of a measured baseline AB. This problem becomes somewhat simpler if:

Draw a circle around the point C, with radius r, passing through A and B (drawing above). Since the angle α is so small, the length of the straightline "baseline" b (drawing on the right; distance AB renamed) is not much different from the arc of the circle passing A and B. Let us assume the two are the same (that is the approximation made here). The length of a circular arc is proportional to the angle it covers, and since 
2π r covers an angle 360° we get and dividing by 2π
Therefore, if we know b, we can deduce r. For instance, if we know that α = 5.73°, 2 π α = 36° and we get Estimating distance outdoorsHere is a method useful to hikers and scouts. Suppose you want to estimate the distance to some distant landmarke.g. a building, tree or water tower.The drawing shows a schematic view of the situation from above (not to scale). To estimate the distance to the landmark A, you do the following:


Curators: Robert Candey, Alex Young, Tamara Kovalick
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