Rational Trigonometry/1

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Why Trig is so Hard
Supposedly, one can measure all the aspects of a triangle with a ruler and protractor. (Actually, given three or four of the three sides and three angles, a triangle is uniquely determined.) But measuring angles accurately is usually impossible. There are three laws which must be learned: Also extremely useful are the Sine-Area formulas, and Heron's Formula.
 * The Sum of Angles is 180º/π
 * The Law of Sines
 * The Law of Cosines

Euclid knew that angles and distances are quite difficult to encapsulate, so he avoided them. Most distances are square-roots, and require infinite work to exhibit fully. Angles are proportional to arc-length, another irrational quantity most difficult to use. Also, use of the circular functions is restricted to calculators and rounding. This trickiness is hidden with the use of square-root symbols, the symbol π, and "soft" examples which only use 30º, 45º, and 60º. Then, there are dozens of trigonometry formulas/identities.