Question
Fri May 06, 2011 By:

if angle B and angle Q acute angles such that sin B = sin Qthen prove that angle B=angle Q

Expert Reply
Thu May 05, 2011
It is given that sin B = sin Q
Clearly, since B and Q are acute angles, angle B = angle Q.
(As sine of two acute angles will be equal if and only if they are both equal)
 
You can prove this also by considering a right triangle ABQ.
Since, B and Q are acute angles, angle B is right angle.
Then, sinQ = AB/AQ
sin B = BQ/ AQ
 
Now, sin B = sin Q implies, AB = BQ
This gives angle B = angleQ
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