Question

If Angle B and angle Q are acute angles such that Sin B equal to sin Q then prove that angle b is equal to angle q?

Answer 1

Consider a ΔABQ having sin B = sin Q .... (1)

Now, in ΔABQ, we have

sin B =AQ/BQand sin Q =AB/BQ

On putting the above values in (1), we get

AQ/BQ=AB/BQ

Therefore, AQ=AB

So, AQ = AB implies that, 

∠B = ∠Q  [Angles opposite to equal sides are equal.] 


REGARDS ...:^: