You and a friend are rowing a boat 8.5 KPH heading north. A cross current is moving 3.2 KPH at an angle of 38 degrees north of the west direction. How fast are you actually moving and what direction are you actually heading?

Answer 1

current north speed = 3.2 sin 38=1.97 N
current west speed = 3.2 cos 38 = 2.52 W

Total North speed = 8.5+1.97 = 10.47
Total west speed = 2.52

tan theta = 2.52/10.47
theta = 13.53 degrees west of north or
47.47 degrees north of west
Is the direction you are GOING (you are still HEADING north (on your compass)). Math teachers do not use proper navigation terminology. They confuse heading, bearing, and course made good.
v = 10.47/cos 13.53 =10.77 kph

Answer 2

Thank you!