mac1147_lecture30_1_c

mac1147_lecture30_1_c - L30 Law of Sines; Law of Cosines;...

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362 a b c α β γ S S S S A A A A A A S S S S S L30 Law of Sines; Law of Cosines; Area of a Triangle A triangle is called oblique if none of the angles is the right angle. Law of Sines sin sin sin abc βγ == Law of Cosines 22 2 2c o s ca b a b = +−
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363 Law of Sines sin sin sin abc α βγ == or sin sin sin a b c β γ h
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364 Example : Solve the triangle: 60 α= ° , 75 β , 9 a = cm. Determine the remaining sides and angle.
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365 b α sin ab = A b a a A Ambiguous Case – ASS Triangle (Given: angle , sides b and a ) 1) If sin = , then we have a right triangle. Indeed, by the Law of Sines, sin 1 = sin 1 β = 9 0 = ° 2) If sin ba b << , then we have two triangles since can be either acute or obtuse angle ( > ), and there are two solutions for : sin sin = sin sin b a β= sin arcsin b a ⎛⎞ = ⎜⎟ ⎝⎠ or sin arcsin b a βπ =−
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366 α b a A b a A 3) If ab > , then β must be an acute angle ( is less than ) and we have one triangle. By the Law of Sines, sin sin = sin sin b a β= sin arcsin b a ⎛⎞ = ⎜⎟ ⎝⎠ 4) If sin < , then we have no triangle.
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This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture30_1_c - L30 Law of Sines; Law of Cosines;...

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