How do I determine angle equality in this graph?

In summary, the conversation was about a graph in a physics textbook that the speaker was having trouble understanding. They were missing something in their understanding of trigonometry and couldn't figure out how to connect two angles in the graph. Another person explained that by extending a line and creating a smaller triangle, the angles could be related through the interior angle sum. The conversation also touched on the difficulty of understanding scientific terms in a second language. Overall, the conversation provided a helpful explanation for understanding the graph.
  • #1
Const@ntine
285
18
Okay, this might be a tad silly, but I cam across this graph/picture i my physics textbook, and for the life of me I can't figure out how to connect the two angles. Here, have a look:

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It's not a big part of what the paragraph is about, so in theory I could just skip it, but it's been killing me to not know! Granted, I haven't brushed up on my Trig. for about, what, 3 years now (aside from the basic stuff that I've so far used in First Year Undergrad Physics and Math), so I'm probably missing something.

I tried drawing the "triangles" and trying to find out if there are any opposite/alternate equal angles, but... nothing. The book itself doesn't even mention it beyond the graph, it just takes the equality for granted.

Any kind of help is appreciated!
 
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  • #2
Continue the line where the "R" is until it its the tangent to the circle, then you can relate the two angles via the interior angle sum in the newly generated triangle.

Overall this is one of the standard diagrams to relate angles to each other, but I remember how it is called.
 
  • #3
mfb said:
Continue the line where the "R" is until it its the tangent to the circle, then you can relate the two angles via the interior angle sum in the newly generated triangle.

Overall this is one of the standard diagrams to relate angles to each other, but I remember how it is called.
Sorry to ask this, but... could you go a bit more in-depth? From what I understand, that's what you're talking about, right?
SWhvs.&token=536700ef-92a9-4a2d-ac45-79f45f3dfe64&owa=outlook.live.com&isc=1&isImagePreview=True.jpg

But I don't see how I can relate the angles of the triangle, and the angle which is created by the "circle" and the tangent.
 
  • #4
That is the basic diagram, right.

The angle in the upper left corner is ##\frac \pi 2 - \theta## via the angle sum in the large triangle.

Continue the tangent until it reaches the horizontal tangent. Via the angle sum in the small triangle, the angle between the two tangents is ##\frac \pi 2 - \left(\frac \pi 2 - \theta\right) = \theta##.
 
  • #5
mfb said:
That is the basic diagram, right.

The angle in the upper left corner is ##\frac \pi 2 - \theta## via the angle sum in the large triangle.

Continue the tangent until it reaches the horizontal tangent. Via the angle sum in the small triangle, the angle between the two tangents is ##\frac \pi 2 - \left(\frac \pi 2 - \theta\right) = \theta##.

Ah, so I draw another tanget, thus creating a smaller triangle, like this:

kc1v0.&token=c0d82f73-3ca7-40f9-bd96-afe1ba4c01a6&owa=outlook.live.com&isc=1&isImagePreview=True.jpg


Yeah, I was focused on just the big triangle and forgot all about the smaller one. Well, that's quite embarassing...

Either way, thanks a ton for the help, twas driving me mad! And I guess I have to brush up on Geometry some time...
 
  • #7
mfb said:

Ah, so that's the general diagram. Thanks (saved)!

The above one (at my RE) is correct for the "matter at hand" though, right?

PS: English isn't my First Language, so there might be some problems when "converting" the info from English to my native one.
 
  • #8
Darthkostis said:
The above one (at my RE) is correct for the "matter at hand" though, right?
Sure.
Darthkostis said:
PS: English isn't my First Language
Same here.
 
  • #9
mfb said:
Sure.

Whew, thank goodness!

mfb said:
Same here.

It's a bit of a hurdle, isn't it? I mean, sure, there are special dictionaries for scientific terms, but still.

Either way, thanks a ton for the help!
 

Related to How do I determine angle equality in this graph?

1. What is the definition of angle equality?

Angle equality refers to the concept that two angles are considered equal if they have the same measure or degree. This means that they have the same amount of rotation about their vertex and their sides are in the same position.

2. How do you prove angle equality?

Angle equality can be proven through various methods, including using the properties of angles (such as the angle addition postulate or vertical angles theorem), congruent triangles, or algebraic equations.

3. What are some examples of angle equality?

Examples of angle equality include two angles that are vertical angles, two angles that are corresponding angles in parallel lines, or two angles formed by intersecting lines. In each of these cases, the angles have the same measure and are therefore considered equal.

4. What is the difference between angle equality and angle congruence?

While angle equality refers to two angles having the same measure, angle congruence refers to two angles having the same measure and shape. This means that not only are the angles equal, but their sides and angles are also identical.

5. Why is angle equality important in geometry?

Angle equality is important in geometry because it allows us to accurately measure and compare angles. It also helps us to identify relationships between angles and use them in geometric proofs and constructions.

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