Posted by **Kourt** on Friday, February 18, 2011 at 2:12pm.

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?

- Math- Please Help!! -
**Greg**, Friday, February 18, 2011 at 4:12pm
739 kilometers per hour. I used an online electronic flight computer.

- Math- Please Help!! -
**Reiny**, Friday, February 18, 2011 at 4:56pm
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

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