Why is this certain angle 20 degrees?

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Discussion Overview

The discussion revolves around the geometry of angles in a problem involving two ships, A and B, and the relationship between their bearings and vector representations. Participants are trying to understand why a specific angle, labeled as 20 degrees, is assigned to the vector from ship A to ship B (VB/A) in the solution diagram.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the assumption that the angle of VB/A is 20 degrees, suggesting that it is not clear how this angle is derived from the diagram.
  • Another participant states that the bearing of ship A towards ship B is given as 20 degrees East of North, implying that this should correspond to the angle in question.
  • Several participants express confusion about the geometric representation of the angles, particularly how VB/A relates to the angle of VA and why it is considered to be 20 degrees.
  • One participant acknowledges a misunderstanding regarding the angle VB/A, indicating uncertainty about its geometric proof.
  • Another participant suggests that the solution triangle is a rearrangement of the initial configuration, questioning why the angle would change if both vectors start at 20 degrees.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the geometric interpretation of the angle VB/A. There are multiple viewpoints regarding its value and the assumptions made about the angles in the solution diagram.

Contextual Notes

Participants express uncertainty about the geometric relationships and the assumptions underlying the angle measurements, indicating a need for clarity on how these angles are defined and proven within the context of the problem.

elementG
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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 VB/A 20 degrees from the solution diagram? It would seem that I had to know that direction of VB/A had the same angle as VA 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.
 
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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.
 
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 VB/A also 20 degrees down from horizontal? Sorry for the confusion!
 
elementG said:
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 VB/A also 20 degrees down from horizontal? Sorry for the confusion!

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

I'd assumed we only care about angle theta, which is 20.
 
VB/A comes off the head of VA. I just don't see how its 20 degrees when VB/A and VA are connected as seen on the solutions diagram.
 
elementG said:
VB/A comes off the head of VA.
Sorry, I hadn't looked at the second diagram.
elementG said:
I just don't see how its 20 degrees when VB/A and VA 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?
 
Oh, I guess I made the wrong assumption. I was assuming the angle that VB/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 VB/A and I label as an unknown, how would I geometrically prove that the angle is 20 degrees?
 
elementG said:
Oh, I guess I made the wrong assumption. I was assuming the angle that VB/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 VB/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.
 

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