Question

In ∆abc and ∆pqr if angle a and angle p are acute angles such that sin a = sin P then prove angle a is equal to angle P​

Answer 1

SOLUTION :

Given Sin A = Sin P

$\sin(A) = \frac{BC}{AC}$

$\sin(P) = \frac{QR}{PQ}$

Then ,

$\frac{BC}{AC} = \frac{QR}{PQ}$

Let ,

$\frac{BC}{AC} = \frac{QR}{PQ} = k$

By using Pythagoras theorm ,

$\sqrt{\frac{AC^2-BC^2}{PQ^2-QR^2}}$

It gives ,

$\frac{AC}{PQ}$

Hence ,

$\frac{AC}{PQ} = \frac{AB}{PR} = \frac{BC}{QR}$

Then ∆ABC is equal to ∆PQR

Therefore , angle A is equal to angle P