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1. A right triangle is____________________ an equilateral triangle
1. A right triangle is____________________ an equilateral triangle

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... which is outside the two triangles. Angle ABD is 60 degrees. Angle CBE is 50 degrees. These two angles sum to 110 degrees. This makes Angle ABC 70 degrees because the three angles form line DE, which is 180 degrees. The correct answer is K. ...
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DEF, ∆ ∆ AB CA . DE FD =

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Notes on Mathematics II

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Rational trigonometry

Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales. His ideas are set out in his 2005 book Divine Proportions: Rational Trigonometry to Universal Geometry. According to New Scientist, part of his motivation for an alternative to traditional trigonometry was to avoid some problems that occur when infinite series are used in mathematics. Rational trigonometry avoids direct use of transcendental functions like sine and cosine by substituting their squared equivalents. Wildberger draws inspiration from mathematicians predating Georg Cantor's infinite set-theory, like Gauss and Euclid, who he claims were far more wary of using infinite sets than modern mathematicians. To date, rational trigonometry is largely unmentioned in mainstream mathematical literature.
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