Vector Components for Destination Distance

[Ellipses]

Homework Statement

Amy wants to reach a destination that is 330m [E31 degrees N] from where she is. She travels a distance b towards [E20 degrees N] and then 100m to her destination. What is the distance b? (list all possible answers)

(Sorry I don't know how to get symbols)

Let [N] and [E] be positive.
delta d = 330m [E31 degrees N]
delta db = x [E20 degrees N]
delta dc = 100m [?]

Homework Equations

dx = d cos theta
dy = d sin theta

theta = tan^-1 (y / x)

The Attempt at a Solution

Well, first, I'm not allowed to use trig to solve (so no sine law for me). When I did it just to get the answer, I came up with x = 246 or x = 401.5 (approximate).

I've been trying this all of yesterday and I've got nothing. At this point I'm just randomly plugging things in and hoping something will come out.

I found the vector components of d, so
dx = +330cos31
dx = +282.87

dy = +330sin31
dy = +169.96

The rest of what I did is just kind of nonsense, now that I look at it. Anyone have any idea how to go about this? Any help would be appreciated! (And I know it probably isn't very clear so if any clarification is needed, just ask!)

 

[Spinnor]

Have a picture of what is going on and the solution might follow?

 

[Ellipses]

Thank you for the picture, but every time I look at it (or my own diagrams), I still can only think of using trig to solve it. I just can't see how you can use components for this. :/

 

[Spinnor]

The problem asks for possible values of b. Does it tell you how you are to solve the problem? If you can solve the problem with trig then go for it?

 

[Ellipses]

I have to use vector components. My teacher said no trig/sine law/anything. D:

 

[Spinnor]

Part of your information is angles, without trig I don't see how you get components? Can you solve this problem graphically with protractor and ruler? Then you could measure the components.

I'm stumped, sorry I'm of no help right now.

Anyone else?