right angle triangle problem

[fiery123]

A ship sails 12km on a bearing of 250, then changes course to a bearing of 135, and sails a further 18km. Find the bearing it would need to sail on, and the distance it would need to travel, inorder to get back to its starting point.

[Glaysher]

Draw a clear diagram

Horizontally

Moves left 12 sin 70
Moves right 18 cos 45

To move back to start move left 18 cos 45 - 12 sin 70

Vertically

moves down 12 cos 70
moves down 18 sin 45

To move back to start move up 12 cos 70 + 18 sin 45

To get distance use Pythagoras on right angled triangle with hypotenuse unknown and other sides 12 cos 70 + 18 sin 45 and 18 cos 45 - 12 sin 70

To get bearing do the inverse of tan on (18 cos 45 - 12 sin 70)/(12 cos 70 + 18 sin 45)

Then subtract this angle from 360

Remember bearings are written as three figures

[fiery123]

ok it was extremely confusing at first since i have no idea where the right angle came in, but i suppose you drew a straight line from the 45 angle to the right, and then down to the point after the 18km was travelled. But anyway after that i managed to work it out.

[Glaysher]

Sorry. Didn't have time to draw a diagram