Question

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~

Answer 1

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.