SOLUTION: SinA =0.1 cos B=0.4 sin C=.7 what is the answer sin(A+B)?

Algebra ->  Trigonometry-basics -> SOLUTION: SinA =0.1 cos B=0.4 sin C=.7 what is the answer sin(A+B)?      Log On


   

Question 806507: SinA =0.1 cos B=0.4 sin C=.7 what is the answer sin(A+B)?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
SinA =0.1 cos B=0.4 sin C=.7 what is the answer sin(A+B)?
***
Identity: sin(A+B)=sinAcosB+cosAsinB
cosA=√(1-sin^2A)=√(1-(.1^2)=√1-.01)=√.99
sinB=√(1-cos^2B)=√(1-(.4^2)=√1-.16)=√.84
sin(A+B)=sinAcosB+cosAsinB=0.1*0.4+√.99*√.84=.04+√.8316
..
Check: (w/calculator)
sinA=0.1
A≈5.7392˚
cosB=0.4
B≈66.4218˚
A+B≈72.1610˚
sin(A+B)=sin(72.1610)≈0.9519
exact value as calculated=.04+√.8316≈0.9519