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0|0|0|||||%281%29sine and %282%29cos proofs of Pythagorean Theorem|wongcheokwan|1|07:31:40|01/19/2007| Thanks for Alexander Bogomolny%27s kind reply to my%0D%0A previous note.%0D%0A%0D%0A 1%29cosine proof%3AWith the usual diagrams and notations.%0D%0A              In TRIANGLE ABC%2Cangle C%3D90deg.%0D%0A              side a is opposite Angle A%0D%0A              side b is opp angle B%0D%0A              side c is opp angle C%0D%0A  From angle C drop a perpendicular to line AB at D.%0D%0A  BD%3Da.cos.B.. DA%3Dc-a.cos.B%0D%0A  cos.A%3Db%2Fc%3D%28c-a.cos.B%29%2Fb....and cos.B%3Da%2Fc%0D%0A  %3A%3A b.b%3Dc.c-ac.cos.B %3Dc.c-ac.a%2Fc%0D%0A  %3A%3A b.b%3Dc.c-a.a    %3A%3Ab2 %2Ba2%3Dc2%0D%0A%0D%0A 2%29sine proof%3ABD%3Da.sin.A ...angle DCB is size A%0D%0A                            angle CDB is 90.deg.%0D%0A  DA%3DBA-BD...Angle ACB is of sizeB.%0D%0A             sin.B%3DDA%2FAC%3D%28c-a.sin.A%29%2Fb%3Db%2Fc%0D%0A             sin.A%3Da%2Fc  %3A%3Acc-ca.a%2Fc%3Dbb  %3A%3Acc-aa%3Dbb%0D%0A%0D%0A these steps are derived from similar triangles.%0D%0A%0D%0A Thanks to readers%0D%0A%0D%0A  %0D%0A%0D%0A