I have a physics question and I'm not sure what to do with the magnitudes?

Question

Here is the info...
d1=28m(W37S), d2=40m(W53N)

The thing is I must use the cosine law to determine the diplacement....BUT I'm having trouble to get the cosC because I don't know what to do with the magnitudes since there are two...please help me

then that makes cos90...which equals zero and that cant be right...cuz the answer at the bak of book is 49

Answer 1

Using law of cosines makes life simpler than breaking it down into x and y components. So: you have 2 angles, so you can infer the third as 180-37-53. That's the side opposite of the magnitude you want. So you have:
x^2 = 28^2 + 40^2 -2x40x80xcos(angle you got from subtraction)
Because the right-hand side is basically a #, you can just square root it to get x.

Answer 2

Did you work out what J Z gave you? Try it.

x^2 = 28^2 + 40^2 - 2x40x80xcos90