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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.

### 1 Answer by Expert Tutors

Scott H. | Engineering/Math/Science Tutor in Newmarket/OnlineEngineering/Math/Science Tutor in Newmar...
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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'