# Homework Help: Direction and Sailing

1. Sep 19, 2006

### Soaring Crane

A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, then 3.50 km southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point.

Find the magnitude of the third leg of the journey.
Find the direction of the third leg of the journey.

I found the magnitude of the third leg. My question is the third leg's direction. The direction in degrees must be expressed in degrees east of north. I do not exactly understand how I am to express it like that. All I know is that if one takes the arctan of the ratio of the third leg's y_component/x_component the answer is wrong.

Thanks.

2. Sep 19, 2006

### Hootenanny

Staff Emeritus
Your almost there. Have you drawn a diagram? Take a closer look at the ratio y_component/x_component . Which angle with this give you? Which angle do you need?

3. Sep 19, 2006

### Soaring Crane

The third leg is a right triangle's hypotenuse. The angle that was found with the mentioned ratio is horizontal from the rt. angle. Does that mean I subtract the angle found with that ratio from 90 degrees to find the third angle of the triangle?

4. Sep 19, 2006

### Hootenanny

Staff Emeritus
Yes, you can do that or you can simply find the arctan of the inverse ratio (x/y).