Very simple Vector Problem - confused by 3 vectors

[07triumphd675]

Very simple Vector Problem -- confused by 3 vectors...

Homework Statement

A commuter plane starts from an airport and takes the route: It first flies to City A located 175 km away in a direction of 30 degrees north of east. Then it flies for 150 km 20 degrees west of north to City B. Finally the plane flies for 190 km due west to City C. Find the location of City C relative to the location of the starting point.

Homework Equations

Ax = Cos(x)(a)
Ay = Sin(y)(a)

So on and so forth --- all the way through Cx = Cos(x)(c) and Cy =Sin(y)(c)

The Attempt at a Solution

The problem is pretty easy to me and I would draw you a picture but I don't have paint on my Mac. Mainly, I'm confused is that there are 3 vectors given here and you are to find the Resultant vector from A ---- > C. I'm used to just two vectors and then finding the resultant vector from A ---- > B. What do you do when you've got an additional vector there? The pythagorean theorem will not work. Any ideas?

 

[cepheid]

add the three vectors *component-wise* and then use pythagoras on the components of the resultant.

 

[07triumphd675]

Ohhh so add Ax + Bx + Cx and then Ay + By + Cy and then use the Pythagorean theorem accordingly.

Wala. Thank-you!