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Дата изменения: Unknown Дата индексирования: Sat Dec 22 09:31:57 2007 Кодировка: Поисковые слова: п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п |
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![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() to Galileo ![]() ![]() ![]() and First Law |
![]() "Pre-Trigonometry"Section M-7 describes the basic problem of trigonometry (drawing on the left): finding the distance to some far-away point C, given the directions at which C appears from the two ends of a measured baseline AB. This problem becomes somewhat simpler if:
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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 straight-line "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 |
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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 |
Then open the eye you had closed (A') and close the one (B') with which you looked before, without moving your thumb. It will now appear that your thumbnail has moved: it is no longer in front of landmark A, but in front of some other point at the same distance, marked as B in the drawing. Estimate the true distance AB, by comparing it to the estimated heights of trees, widths of buildings, distances between power-line poles, lengths of cars etc. The distance to the landmark is 10 times the distance AB.
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