A ship leaves port with a bearing of S 40 W. After traveling 7 miles, the ship turns 90 degrees on a bearing of N 50 W for 11 miles. At that time, what is the bearing of the ship from port?

Answer 1

using the usual trig orientation, with due East as 0°

S40W = 220°
N50W = 140°

so,starting at (0,0) after the first 7 miles, the ship is at (7cos220°,7sin220°) = (-5.36,-4.50)

Next from there it proceeds another (11cos140°,11sin140°) = (-8.43,7.07)

It is now at (-13.79,2.57)
distance = 14.03 miles
tanx = 2.57/-13.79 = 180-10.55°
bearing from port is W10.55°N