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10 cards from this deck
Area=12bcsinA\text{Area} = \frac{1}{2}bc \sin AArea=21bcsinA
Two sides and the included angle known
Angle that lies between two known sides
asinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}sinAa=sinBb=sinCc
Two angles + one side, or two sides + non-included angle
Two possible triangles satisfy given conditions
a2=b2+c2−2bccosAa^2 = b^2 + c^2 - 2bc \cos Aa2=b2+c2−2bccosA
Two sides + included angle, or all three sides known
cosA=b2+c2−a22bc\cos A = \frac{b^2 + c^2 - a^2}{2bc}cosA=2bcb2+c2−a2
Becomes Pythagoras' theorem: a2=b2+c2a^2 = b^2 + c^2a2=b2+c2
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