Why is this certain angle 20 degrees?

In summary, the problem involves finding the angle from VB/A in a given solution diagram. The angle is given as 20 degrees and is necessary to solve the problem. Without this information, the problem cannot be solved.
  • #1
elementG
21
1

Homework Statement


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

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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  • #2
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.
 
  • #3
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!
 
  • #4
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.
 
  • #5
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.
 
  • #6
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?
 
  • #7
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?
 
  • #8
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.
 

1. Why is this certain angle 20 degrees?

The angle of 20 degrees is determined by the intersection of two lines or surfaces, where each line or surface forms a 20-degree angle with the other. This angle is a measurement of the amount of rotation between the two lines or surfaces.

2. How is the angle of 20 degrees calculated?

The angle of 20 degrees is typically calculated using a protractor or other measuring tool. It can also be calculated using trigonometric functions such as sine, cosine, and tangent.

3. What is the significance of a 20-degree angle in geometry?

A 20-degree angle is considered an acute angle, meaning it is less than 90 degrees. It is also considered a relatively small angle, making it useful in various geometric constructions and measurements.

4. Can a 20-degree angle be found in nature?

Yes, a 20-degree angle can be found in nature, such as in the shape of a seashell or the angle of a leaf's veins. It can also be seen in the angles of crystals and snowflakes.

5. How does the angle of 20 degrees affect the properties of a shape?

The angle of 20 degrees can affect the properties of a shape by determining its symmetry, the number of sides it has, and its overall stability. It can also affect the angles of other shapes when combined in a larger structure.

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