(Q10) If ∠A and ∠p are acute angles such that sin A =sin P then prove that ∠A=∠P
A
B
C
P
R
Q
Given sin A=sin P
From △ABC,sin A=
BC
AC
From △PQR,sin
QR
PQ
Then
BC
AC
=
QR
PQ
Let,
BC
AC
=
QR
PQ
=k
By using Pythagoras theorem
AB
2
PR
2
=
AC
2
- BC
2
PQ
2
- QR
2
AB
2
PR
2
=
2
2
AB
PR
=
AC
PQ
=
AB
PR
=
BC
QR
then△ABC~△PQR
∠A=∠P
clear