Hello, takkun0486!
Here's #2 . . .
2. A ship sails for 25 miles on a bearing of 225°,
then turns and sails on a bearing of 300° for 16 more miles.
a) How far is the ship from its starting point?
b) At what bearing does the ship end up with respect to where it started? A sketch is always welcome. Code:
| A
*
b * * |
* *45°|
* * |
C * : * |
* : * c=25 |
a=16 *60°:45°* |
* : *
*
B
The ship starts at A, sails southwest for 25 miles to point B.
Then heads 60° west of north for another 16 miles to point C.
a) We want side b = AC.
Law of Cosines: . b² .= .16² + 25² - 2(16)(25)cos105° .= .1088.066236
Therefore: .b .≈ .33 miles.
b) We want angle A.
. . . . . . . . . . . . . . . . . . . .b² + c² - a² . . . 33² + 25² - 16²
Law of Cosines: . cos A .= .--------------- .= .------------------- .= .0.883636364
. . . . . . . . . . . . . . . . . . . . . . 2bc . . . . . . . . .2(33)(25)
Hence: .A .≈ .28°
Therefore, the ship is at a bearing of: .225° + 28° .= .253°