Question

An airplane has an airspeed of 724 kilometers per hour at a bearing of 30 degrees.The wind velocity is 32 kilometers per hour from the west. What are the groundspeed and the direction of the plane?

Answer 1

739 kilometers per hour. I used an online electronic flight computer.

Answer 2

make a diagram.
from the origin draw a vector with a bearing of 30 degrees and mark its length 724. Call it OA
Draw a horizontal line AB of length 32
the angle OAB = 120 degrees

by cosine law:
OB^2 = 724^2+32^2-2(724)(32)cos120
= 548368
OB= 740.5

now by the Sine Law:
sinO/32 = sin120/740.5
sinO= .0374235
angleO=2.145
so the bearing is 30+2.1 or 31.1 degrees, and the ground speed is 740.5 km/h

check my arithmetic