Bearing and Distance????

Question

After leaving an airport, a plane flies for 2 hours on a course of 70° at a speed of 200 km/h. The plane then flies for 3 hours on a course of 210° at a speed of 150 km/h. Use this information to determine the bearing and distance of the airport from the plane.

 

Determine the Distance and the Bearing.

Answer 1

400 km at 70 degrees

then 450 km at 210 degrees

angle A = 70-(210-180)=40

construct a triangle and use the law of cosines

SAS 450-40 degrees - 400

d= distance from plane to airport

d^2=450^2+400^2-2(450)(400)Cos40

d= sqr(202500+160000- 360000Cos40=sqr86,724.00048

d= 294.489 km

use law of sines to find angle opposite 450 km

sinB= 450sin40/294.489

B=79.891

subtract 70

= 7.891 degrees bearing