Posted by sandra on Tuesday, January 10, 2012 at 11:52am.
As usual, draw a diagram.
the distance is easy, since we have a right triangle
d^2 = 15^2 + 12^2 = 369
d = 19.2
The bearing is N (33+x) W where
tan x = 12/15
x = 37°
bearing is N 70° W
Alternatively, and with much more work,
(0,0) + (15 cos 123°,15 sin 123°) = (-8.17,12.58)
(-8.17,12.58) + (12 cos 213°, 12 sin213°) = (-8.17,12.58) + (-10.06,-6.54) = (-18.23,6.04)
d^2 = 369
tan x = -18.23/6.04 = -3.02
x = 180-20 = 160° = N 70° W
oops
tan x = 6.04/-18.23