Question:
if angle B and angle Q are acute angles such that sin B= sin Q,prove that angle B=angle Q
Answer:
Let us suppose that ABQ is a right angle triangle such that triangle is right angled at B.
Given
sinB = sinQ
Now
sinB = AQ/BQ ...........1
sinQ = AB/BQ ...........2
Since sinB = sinQ
then from equation 1 and 2, we get
AQ/BQ = AB/BQ
=> AQ = AB
Therefore triangle ABQ is isoscales triangle.
So Angle B = Angle Q
Hense proved.
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