Help with adding vectors with component method (sin/cos/tan)

[amd123]

Homework Statement

A ship leaving its port sails due north for 30 miles and then 50 miles in a direction of 60 degrees east of north. At the end of this displacement, where is the ship relative to its port?

An army recruit on a training exercise is instructed to walk on a bearing of 6.3 degrees north of west for 5 miles, then on a bearing of 41 degrees north of east for 4 miles, and finally on a bearing of 15 degrees west of north for a direction of 3 miles. Determine the distance and direct the recruit must walk to return to his starting position?

Homework Equations

What is the difference between let's say North of West and West of North and how does this make my drawing of the triangles different? Because for these two problems my teacher said I have my x and y values reversed because of how I drew the triangles because of the description of the direction.

I know I'm doing the sin/cos/tan functions correctly but I get my values in the opposite places X for Y and vice versa because of the north of west and west of north concept.

Can someone please explain it to me?

The Attempt at a Solution

http://img231.imageshack.us/my.php?image=77107532lx7.jpg
http://img231.imageshack.us/my.php?image=74381618jo2.jpg
according to my teacher my answers are wrong... what am i doing wrong?

 

[asleight]

Homework Statement

A ship leaving its port sails due north for 30 miles and then 50 miles in a direction of 60 degrees east of north. At the end of this displacement, where is the ship relative to its port?

An army recruit on a training exercise is instructed to walk on a bearing of 6.3 degrees north of west for 5 miles, then on a bearing of 41 degrees north of east for 4 miles, and finally on a bearing of 15 degrees west of north for a direction of 3 miles. Determine the distance and direct the recruit must walk to return to his starting position?

Homework Equations

What is the difference between let's say North of West and West of North and how does this make my drawing of the triangles different? Because for these two problems my teacher said I have my x and y values reversed because of how I drew the triangles because of the description of the direction.

I know I'm doing the sin/cos/tan functions correctly but I get my values in the opposite places X for Y and vice versa because of the north of west and west of north concept.

Can someone please explain it to me?

The Attempt at a Solution

http://img231.imageshack.us/my.php?image=77107532lx7.jpg
http://img231.imageshack.us/my.php?image=74381618jo2.jpg
according to my teacher my answers are wrong... what am i doing wrong?

Let's say that the x-axis runs in the E-W direction and the y-axis in the N-S direction. Then, 30 miles north of west would be 30 units above the -x axis, with the angle between the line connecting the origin and the point and the -x axis being your desired angle.

 

[amd123]

there i posted my work