Asked by Melinda
                Vector C=5 and Vector D=8. The angle formed by  C and D is 35 degrees, and the angle formed by A and C is 40 degrees. Determine |B|.
Here is the image for triangle:
imgur dot com/OZAwV
please help, I have a test tomorrow~
            
        Here is the image for triangle:
imgur dot com/OZAwV
please help, I have a test tomorrow~
Answers
                    Answered by
            Reiny
            
    Since you are dealing with the magnitude of the vectors, we can use basic geometry.
Using the cosines law on the first triangle ...
(2A)^2 = 5^2 + 8^2 - 2(5)(8)cos 35°
= 89 - 65.53216...
= 23.4678...
2A = √23.4678.. = 4.84436...
A = √23.4678.. /2 = 2.42218... (store in calculator's memory)
At this point there is a contradiction in your information
Using the sine law we can now find the angle formed between vectors 2A and C, and that makes the angle between A and C appr. 71° , not 40° like you said.
Anyway, we found the magnitude of vector 2A to be appr. 4.844
Once you find the typo, you can proceed from there.
    
Using the cosines law on the first triangle ...
(2A)^2 = 5^2 + 8^2 - 2(5)(8)cos 35°
= 89 - 65.53216...
= 23.4678...
2A = √23.4678.. = 4.84436...
A = √23.4678.. /2 = 2.42218... (store in calculator's memory)
At this point there is a contradiction in your information
Using the sine law we can now find the angle formed between vectors 2A and C, and that makes the angle between A and C appr. 71° , not 40° like you said.
Anyway, we found the magnitude of vector 2A to be appr. 4.844
Once you find the typo, you can proceed from there.
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