Hello, I have a question on a bearing problem. Here's the problem:
A ship sails a distance of 76 miles in the direction S 42° E and then sails a distance of 90 miles in the direction N 48° E. Find the distance of the ship's final position from its original position and the bearing and azimuth of the ship's final position.
My issue here is that I don't really know how to start the problem. I know how to draw the bearing of S 42° E, but I'm not quite sure what to do with the N 48° E.
I also have another problem that I need help on. I attempted it, but the book has a different answer than the one that I have. Here's the problem:
A DC-9 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N 40° E. After flying for 1/2 mile, the pilot requests permission to turn 90° and head toward the southeast. The permission is granted. After the airplane goes 1 mile in this direction, what bearing should the control tower use to locate the aircraft?
Here is my attempt at solving the problem:
tan(x) = 1/(1/2)
tan(x) = 2
x = tan^-1(2)
x = 63.4°
63.4° - 40° = 23.4°
So my answer was S 23.4° E. However, the book says that the answer is S 76.6° E. Can anyone explain what I did wrong?