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Pre-Calc Exam Notes 52

# Pre-Calc Exam Notes 52 - 52 Chapter 2 General Triangles 2.3...

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52 Chapter 2 General Triangles §2.3 Note that in any triangle ABC , if a = b then A = B (why?), and so both sides of formula (2.17) would be 0 (since tan 0 = 0). This means that the Law of Tangents is of no help in Case 3 when the two known sides are equal . For this reason, and perhaps also because of the somewhat unusual way in which it is used, the Law of Tangents seems to have fallen out of favor in trigonometry books lately. It does not seem to have any advantages over the Law of Cosines, which works even when the sides are equal, requires slightly fewer steps, and is perhaps more straightforward. 4 Related to the Law of Tangents are Mollweide’s equations : 5 Mollweide’s equations : For any triangle ABC , a b c = sin 1 2 ( A B ) cos 1 2 C , and (2.21) a + b c = cos 1 2 ( A B ) sin 1 2 C . (2.22) Note that all six parts of a triangle appear in both of Mollweide’s equations. For this reason, either equation can be used to check a solution of a triangle. If both sides of the equation agree (more or less), then we know that the solution is correct.
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