SOLUTION: If sin A = 4/5, tan B = 5/12, and A and B are first quadrant angles, what is the value of sin(A+B)?

Algebra ->  Trigonometry-basics -> SOLUTION: If sin A = 4/5, tan B = 5/12, and A and B are first quadrant angles, what is the value of sin(A+B)?      Log On


   

Question 949519: If sin A = 4/5, tan B = 5/12, and A and B are first quadrant angles, what is the value of sin(A+B)?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If sin A = 4/5, tan B = 5/12, and A and B are first quadrant angles, what is the value of sin(A+B)?
***
sinA=4/5
cosA=3/5 (working with a 3-4-5 reference right triangle in quadrant I)
tanB=5/12
sinB=5/13 (working with a 5-12-13 reference right triangle in quadrant I)
cosB=12/13
..
sin(A+B)=sinAcosB+cosAsinB=4/5*12/13+3/5*5/13=48/65+15/65=63/65
sinA=4/5
A=53.13˚
tanB=5/12
B=22.62˚
A+B=75.75˚
sin(A+B)=sin 75.75≈0.9692
Exact value=63/65≈0.9692 ˚