physics
posted by Melissa .
A triathlete swims 1200 m due to east followed by 1500 m due northeast (45o). What is the overall displacement? (magnitude and angle). Calculate the displacement with longhand calculations.

Long hand? I wonder what that means.
sketch the diagram.
You have two sides, and the included angle. SAS Law of cosines to get the magnitude of the displacement
d^2=1200^2+1500^2+2(1200)(1500)Cos135
solve for displacement magnitude.
Now angle, in my sketch, law of sines:
1500/SinA=d/sin135
you know d, solve for A. But A is measured from East, so the angle from N is 90A. 
thank you bobpursley