A ship is sailing through the water i the English Channel with a velocity of 2 knots along a bearing of 157 degrees. The current has a velocity along a bearing of 213 degrees. The actual velocity of the ship is the vector sum of the ship's velocity and the water's velocity. Find the actual velocity.Ok so i understand how to do the actual problem, I just have no idea how to convert the bearing degrees into standard form so i can do the problem. I looked at my teacher's review and she gave the standard form for the bearing of 157 degrees as 293 degrees, and the 213 degree bearing as 237 degrees. Well I looked at them and found that the both add up to 450 degrees which i thought might be the solution, but I looked at another problem that had a bearing of 60 degrees and standard position of 30 degrees. Thanks for any help in advance.
true bearing is a navigational angle. it is oriented such that 000 is at due north, and it increases clockwise. a mathematical angle is oriented so that 0 is at due east and it increase counter-clockwise. as a result, the relationship between the true bearing and a mathematical angle is A1 = 90 degrees - A2 where if A1 is the navigational angle, then A2 must be the mathematical angle, or if A1 is the mathematical angle, then A2 must be the navigational angle. That's why bearing 157 degrees = 90 - 157 = -67 degrees = -67+360 = 293 degrees and bearing 213 degrees = 90 - 213 = -117 deg = -117+360 = 237 degrees === so as long as you convert bearings into mathematical angles, then you can resolve vectors into (x,y) coordinates using the standard transformation x = r cos(t) y = r sin(t) where r is the magnitude of the vector and t is the mathematical angle. otherwise,you have to use x = r cos(90-t) = r sin(t) y = r sin(90-t) = r cos(t) where t is the bearing
