Vector A has magnitude of 9.77 units and points due east. Vector B points due north.

Question

1) What is magnitude of B, if the vector A+B points 34.7 north of east?

2) Find magnitude of A+B

I am not sure what formulas to use for this. If someone could show me how to start this I will try to solve it myself and then check back to see if I am correct. Thank you!

Answer 1

tanα =B/A,
B =A•tanα = 9.77•tan34.7º =6.77.
cosα = A/(A+B),
(A+B) = A/ cosα = 9.77/cos34.7º = 11.88

Answer 2

Thank you!!