SOLUTION: https://docs.google.com/document/d/1fwlRpNqz5l4Gbc2NvkH3RhcdsyxG3drAzyvOFfMwz48/edit?usp=sharing

Algebra ->  Trigonometry-basics -> SOLUTION: https://docs.google.com/document/d/1fwlRpNqz5l4Gbc2NvkH3RhcdsyxG3drAzyvOFfMwz48/edit?usp=sharing      Log On


   

Question 1193941: https://docs.google.com/document/d/1fwlRpNqz5l4Gbc2NvkH3RhcdsyxG3drAzyvOFfMwz48/edit?usp=sharing
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
law of sines says:
sin(CAB) / 10 = sin(ABC) / 15
you are given sin(CAB) = sqrt(3)/3.
formula becomes:
(sqrt(3)/3) / 10 = sin(ABC) / 15
solve for sin(ABC) to get:
sin(ABC) = (15 * sqrt(3)/3) / 10 = .8660254038.
solve for ABC to get:
ABC = arcsin(.8660254038) = 60 degrees.
since ABC is also theta, then theta = 60 degrees.
since sin(CAB) = sqrt(3)/3, then:
CAB = arcsin(sqrt(3)/3) = 35.26438968 degrees.
2 * CAB = 70.52877937 degrees.
cos(2 * CAB) = cos(70.52877937) = .333333333... = 1/3.
let me know if you have any questions.
theo