- #1
Can You Help Me Find Angle A? - Understanding Sine Calculation
- Context: High School
- Thread starter TSN79
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Discussion Overview
The discussion revolves around the calculation of angle A using trigonometric functions, specifically sine and tangent. Participants are trying to understand the logic behind the provided equation from a textbook and how it relates to the geometry of a drawing involving circles and angles.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant questions the validity of using sine to find angle A, suggesting it might actually be tangent instead.
- Another participant expresses uncertainty about the textbook's claim, implying that the calculation might be incorrect.
- Some participants propose that the angle can be calculated from different reference points, but this does not resolve the confusion about the sine versus tangent issue.
- A later reply provides a method for calculating the opposite side of a right triangle formed by angle A, indicating that the tangent function could be used instead.
- Another participant mentions that the sine value calculated from the picture is approximately .344, suggesting a potential misprint in the book.
Areas of Agreement / Disagreement
Participants express disagreement regarding whether to use sine or tangent for calculating angle A. There is no consensus on the correct approach, and multiple interpretations of the problem remain unresolved.
Contextual Notes
There are limitations regarding the clarity of the drawing and the assumptions made about the relationships between the angles and sides involved. The discussion reflects uncertainty about the definitions and calculations presented in the textbook.
- #2
iNCREDiBLE
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TSN79 said:The drawing below shows an angle A that I'm suppsosed to find. My book does this;
[tex]sin A=\frac{530-160}{2\cdot505}=0,366[/tex]
I am not able to follow the logic in how this would give me the sine of A...would love it if someone could help me out!
Shouldn't it be tan A?
- #3
LeonhardEuler
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Are you sure they don't mean tanA? Thats what it seems like.
- #4
TSN79
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Not according to my book...
- #5
TSN79
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You are able to find the same angle in several places here, I just didn't draw them in, it might be calculated in reference to one of these places...?
- #6
LeonhardEuler
Gold Member
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No, that can't be it. You can calculate sin (A) based on this picture to be about .344. It will be the same no matter where you calculate it from. Either the picture or the equation is a misprint.
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- #9
radou
Homework Helper
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According to the first picture, [tex]sinA=\frac{185}{\sqrt{505^2+185^2}}[/tex] ...
- #10
TSN79
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But it doesn't really matter if it's sin or tan, the angle is the same, but if one you could only tell me the process of your calculation to find it I'd really appreciate that...
- #11
LeonhardEuler
Gold Member
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In the first picture, draw a vertical radius in the upper part of the larger circle. Now extend the bottom line from angle A to meet this radius. This forms a right triangle. The leg adjacent to A has length 505. The length of the opposite side can be calculated because you can see that it is the larger radius minus the smaller radius. That is (1/2)530 - (1/2)160. The tangent of the angle is the opposite over the adjacent side, which, factoring out the (1/2), is the expression given.
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