Law of Cosines and bearings word problems PLEASE HELP ASAP

Question

1) Two planes fly from a point A. The angle between their two flight paths is 42 degrees. one plane has flown 35 miles from point A and the other has flown 20 miles from point A. How far apart are the two planes at this point?

2) A plane flies from A to B on a bearing of N75 degrees East for 810 miles. Then it flies from point B to point C on a bearing of N 32 degrees East for 648 miles. Find the distance from A to C. 

Answer 1

let a = length of first plane flight = 35 miles

let b = length of second flight = 20 miles

C is the angle between the paths = 42 degrees

 

c is the distance between the planes at the new point.

 

Law of Cosines:  c² = a² + b² - 2ab cos (C)

 

= 35² + 20² - 2(35)(20) cos (42)

= 1625 - 700 (0.7431)

= 1625 - 520.2

c² = 1104.8

c = √1104.8

c = 33.24 miles

 

The second part can be solved similarly with the two flight legs making the 'a' and 'b' legs of the triangle and the angle between them being angle 'C'