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 long-hand calculations.

Answer 1

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 90-A.

Answer 2

thank you bobpursley