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In an acute angled triangle,if sin(A+B-C)= 1/2 and cos(B+C-A)= 1/√2, find A,B and C

In an acute angled triangle,if sin(A+B-C)= 1/2 and cos(B+C-A)= 1/√2, find A,B and C

Grade:10

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4407 Points
4 years ago
sin 30=1/2 and cos45= 1/root2
A+B-C=30
B+C-A=45
A+B+C=180
B=75/2
C=75
A=67.5
Ramnath Venkatesh
31 Points
4 years ago
It is given that sin (A+B-C)=1/2 and cos(B+C-A)=1/(root)2
But, sin 30=1/2 and cos 45= 1/(root)2
=>A+B-C=30------(1)
and 
    B+C-A=45-------(2)
from (1) and (2),
A=135/2
B=75/2
C=75
 
 

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