Why is this certain angle 20 degrees?

[elementG]

Homework Statement

Problem #199
http://img88.imageshack.us/img88/8008/scan0001vd.jpg
Solution
http://img21.imageshack.us/img21/2131/199hg.jpg

Homework Equations

Why is the angle from V_B/A 20 degrees from the solution diagram? It would seem that I had to know that direction of V_B/A had the same angle as V_A in terms of the geometry (if two parallel lines are cut by a transversal, its alternating interior angles are equal). I just don't see how you can assume that.

The Attempt at a Solution

Since drawing a triangle is the first part, I don't have any "attempt" at it yet.

 

[DaveC426913]

I'm not sure what you're asking.

You are given that the bearing is 20 degrees. i.e. A takes a bearing of B and sees it is 20 degrees East of North, thus theta is 20 degrees.

 

[elementG]

I saw that 20 degrees was given, I just don't see how the angle is 20 degrees on the solution diagram. Ship A observes ship B at 20 degrees, but how is V_B/A also 20 degrees down from horizontal? Sorry for the confusion!

 

[DaveC426913]

I saw that 20 degrees was given, I just don't see how the angle is 20 degrees on the solution diagram. Ship A observes ship B at 20 degrees, but how is V_B/A also 20 degrees down from horizontal? Sorry for the confusion!

It's been while, sorry, V_B/A represents what part of the diagram?

I'd assumed we only care about angle theta, which is 20.

 

[elementG]

V_B/A comes off the head of V_A. I just don't see how its 20 degrees when V_B/A and V_A are connected as seen on the solutions diagram.

 

[DaveC426913]

V_B/A comes off the head of V_A.

Sorry, I hadn't looked at the second diagram.

I just don't see how its 20 degrees when V_B/A and V_A are connected as seen on the solutions diagram.

Well, the solution triangle is just a rearrangement of the starting configuration. The two vectors start off at 20 degrees, why would that change?

 

[elementG]

Oh, I guess I made the wrong assumption. I was assuming the angle that V_B/A made was not necessarily 20 degrees. I guess I'm confused (a little bit) still is because I can't see it geometrically. Like say for instance, I'm still on the assumption that the angle is not 20 degrees for V_B/A and I label as an unknown, how would I geometrically prove that the angle is 20 degrees?

 

[DaveC426913]

Oh, I guess I made the wrong assumption. I was assuming the angle that V_B/A made was not necessarily 20 degrees. I guess I'm confused (a little bit) still is because I can't see it geometrically. Like say for instance, I'm still on the assumption that the angle is not 20 degrees for V_B/A and I label as an unknown, how would I geometrically prove that the angle is 20 degrees?

You would not be able to solve the problem. You're given the angle because you need it.