private plane A to B

Question

From A to B a private plane flies 2.4 hours at 110 mph on a bearing of 35∘35∘. It turns at point B and continues another 22 hours at the same speed, but on a bearing of 125∘125∘ to point C. Round each answer to three decimal places.

At the end of this time, how far is the plane from its starting point?  miles

On what bearing is the plane from its original location?  degrees

Answer 1

The vector for the first leg is B–A = vt₁(sinθ₁,cosθ₁) and for the second leg is C–B = vt₂(sinθ₂,cosθ₂). From these one can calculate |C–A| and ArcCos((C₂–A₂)/|C–A|).