Posted by Jane on .
An airplane flies 200 km due west from city A to city B and then 240 km in the direction of 31.0° north of west from city B to city C.
(a) In straightline distance, how far is city C from city A?
(b) Relative to city A, in what direction is city C?

College Physics 
Damon,
Law of cosines
b^2 = a^2+c^22ac cos B
b^2 = 240^2 + 200^2 2(240)(200)cos(18031)
solve for b which is distance from A to C
then law of sines
sin A/240 = sin(18031)/b
solve for angle A 
College Physics 
Anonymous,
As a sailboat sails 59.0 m due north, a breeze exerts a constant force 1 on the boat's sails. This force is directed at an angle west of due north. A force 2 of the same magnitude directed due north would do the same amount of work on the sailboat over a distance of just 36.0 m. What is the angle between the direction of the force 1 and due north?

College Physics 
Cory,
because it says the two forces do the same amount of work, you can tell that the two distances given are the hypotenuse and leg of a right triangle. after that it's just a matter of taking the inverse cos of adjacent/hypotenuse