Question
Sat April 02, 2011 By: Akash Chaturvedi

the sines of 2 angle of triangle are equal to 5/13 and 99/101 what is cosine of 3rd angle

Expert Reply
Sat April 16, 2011
Let the angles be A,B and C.
Then A + B + C=180 degrees
=> C = (180- (A+B)) => Cos C = Cos (180- (A+B)) = - Cos(A+B)
 
= -(cos A cos B - sinA SinB) =  sinA SinB -cos A cos B
 
now cos a = sqrt(1-sin^A)= 12/13.
Similarly cos B= 20/101
 
=> Cos C= 5/13 *99/101 - 12/13*20/101= 255/(13*101)
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