Suppose a plane wants to fly due South and can go 180 km/hr in still air.  There is a wind of 30 kilometers per hour blowing from a direction of 35°.  What direction should the plane head and what will be its ground speed?

1. Draw a picture to represent the problem.
2. Calculate the components of the wind vector.
3. Use the components of the wind vector to find the components of the plane's heading vector.
4. Use the components of the heading vector to find the angle of the heading vector.
5. Use the vertical components of the heading and wind vectors to find the planes ground speed.

Alternately, you could draw a picture to represent the problem and then use the Laws of Sine and Cosine to solve the triangle and answer the questions.

The final answers are: The plane needs to head 174.514° and its ground speed is203.750 km/hr.  To see the work that led to the answer

Another good problem to try is number 53 of the departiment final exam review guide.