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**Relative Velocity Problem -- find the angle**

## Homework Statement

An airplane has a cruising speed (speed of plane with respect to the air) of 547 mph. The wind is blowing at 84 mph 40° north of east. The plane needs to fly from Geordi to Data, which is 982 miles at 28° west of north.

Part A: What direction should the plane head to fly straight from Geordi to Data? (° W of N).

Part B: How long does it take for the plane to fly from Geordi to Data? (hours)

## Homework Equations

Law of sines?

## The Attempt at a Solution

http://www.flickr.com/photos/[email protected]/5443668917/

Based on the figure I have made, which is probably incorrect if any pattern can be drawn from the previous 6 hours of failure:

I tried to use law of sines to find alpha:

84/sin(α) = 547/sin(50)

Using the inverse sine I get an angle of 6.76° for α. (This makes no sense as we're given that the direction from Geordi City to Data City is 28 degrees West of North. What is going on here?)

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