Dune buggies X and Y are 500m apart, and the bearing of Y from X is 215degres. X travels 200m due east and Y travels 100m due north. How far apart the dune buggies now?

Answer 1

If X is at the origin, then Y is in quadrant 4.

215 degrees puts Y degrees off the negative y axis and 55 degrees from positive x axis

so the coordinates of Y are:

cos 55 = x /500 ---> x = 500*cos 55 = 286.7882+

and

sin 55 = y / 500 ---> y = 500 * sin 55 = 409.576+

Meanwhile, X moves to (200,0)

Distance formula says:

sqrt ( (286.7882+-200)^2 + (409.576-200)^2) = 418.6702-