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Thread: An interesting solution

  1. #1 An interesting solution 
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    Hi, this is my first post here, so I'm not sure if I'm posting this in the right place, so bare with me.

    A couple of weeks ago my Geometry teacher handed out some extra credit. There was one problem I had a little difficulty. I'm pretty sure because I was overthinking it. We turned the extra credit in today, adn I wanted to know if it was really as hard as it felt or if I was, in fact, over thinking it.

    Here's the problem:



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  3. #2  
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    Angle D is the same as angle BDC.

    Half of angle B + half of angle C +angle BDC=180.

    That ought to get you started.


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    Oh, I already have the answer and was just wondering 1) If there is an actual method to it, and 2) I thought it was an interesting solutinon and was wondering if anyone else found it interesting.

    Thanks anyways, Harold.
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  5. #4 Re: An interesting solution 
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    Quote Originally Posted by lord twiggy1
    Hi, this is my first post here, so I'm not sure if I'm posting this in the right place, so bare with me.

    A couple of weeks ago my Geometry teacher handed out some extra credit. There was one problem I had a little difficulty. I'm pretty sure because I was overthinking it. We turned the extra credit in today, adn I wanted to know if it was really as hard as it felt or if I was, in fact, over thinking it.

    Here's the problem:

    Let a denote the angle at A, c the half-angle at C, b the half-angle at B and d the angle at D.

    Then c + b + d = and 2c + 2b + a = . You can solve these equations to get a = 2d - and so a = 100 degrees
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    where do you get pi from?
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  7. #6  
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    Quote Originally Posted by lord twiggy1
    where do you get pi from?
    The angles of triangle add up to pi. I am surprised that you have not seen that. Angles in mathematics are normally expressed in the natural units of radians. Pi is 180 degrees, but degrees are normally used only for applications such as engineering.
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    Oh really? I did not know that. I thought that pi was 3.14159... Can you explain that to me? Is it both?
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    You will learn that when you take trigonometry. Pi radians is equal to 180 degrees. There's nothing exotic about it.

    If you have a calculator with trig functions it can be in the degree mode or radian mode. You have to be careful to enter your angles in the correct manner for the mode you have selected.
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    Oh, I see. Thank you.
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  11. #10  
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    Quote Originally Posted by lord twiggy1
    Oh really? I did not know that. I thought that pi was 3.14159... Can you explain that to me? Is it both?
    Pi is the ratio between the circumference of a circle and its diameter. That ratio is a trancendental number that is approximately 3.14159.

    Think about a circle of radius 1. The circumference is . Now think about an angle with base on the x-axis. That angle determines an arc on the circle. The length of that arc is a measere of the subtended angle. So, a right angle subtends and arc that is 1/4 of the circle for an arc length of which is 90 degrees or radians. Quite often when speaking of angles in mathematics is just understood that the measure is radians.

    I am a bit surprised that you are using degrees exclusively in a mathematics class. Usually angles are treated in radians and the correspondence with degrees is only brought in so that students who encounter degrees in engineering or physics applications later on don't get confused. Degrees are the common unit for such applications, but when you study trigonometric functions it is essential to be able to think in terms of radians.
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    Quote Originally Posted by DrRocket
    I am a bit surprised that you are using degrees exclusively in a mathematics class. Usually angles are treated in radians and the correspondence with degrees is only brought in so that students who encounter degrees in engineering or physics applications later on don't get confused.
    Doc, I'm surprised that you're surprised. I recall using degrees in high school geometry class. Every schmo understands angles in degrees before they ever take a high school math class.
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  13. #12  
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    Yeah...I think I saw radians first in pre-calc or maybe trig...trig would probably make more sense.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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  14. #13  
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    We're doing trig in the next chapter, so I'l probably learn about radians soon.

    But anyways, has anyone done my problem and found anything interesting in and ?
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  15. #14  
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    Quote Originally Posted by Harold14370
    Quote Originally Posted by DrRocket
    I am a bit surprised that you are using degrees exclusively in a mathematics class. Usually angles are treated in radians and the correspondence with degrees is only brought in so that students who encounter degrees in engineering or physics applications later on don't get confused.
    Doc, I'm surprised that you're surprised. I recall using degrees in high school geometry class. Every schmo understands angles in degrees before they ever take a high school math class.
    I'm not surprised that they are using degrees. I am surprised that they are using degrees exclusively.

    I agree that every schmo understands angles in degrees. But I thought the educational process would take geometry students beyond the level of every schmo.

    I have to admit that it has been sufficiently long since I took geometry in high school that I am not positive that we used radians, but I think we did. I am dead certain that by the following year we were using radians as a matter of course. It has been a long time, but I think that as soon as I understood what a right angle was I also knew that the angle was .

    I don't remember ever using degrees rather than radians in physics or electrical engineering classes. When I taught trigonometry I taught both radians and degrees and used whichever was most convenient at the time -- degrees are easier when you have to do table look-ups. I don't recall ever using degrees exclusively.
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  16. #15  
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    Quote Originally Posted by lord twiggy1
    We're doing trig in the next chapter, so I'l probably learn about radians soon.

    But anyways, has anyone done my problem and found anything interesting in and ?
    Those angles are what I called b and c. And I did post a solution to your problem earlier. Is that what you were looking for?
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  17. #16  
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    NO, I already knew the answer, I just wanted to see if you noticed anything interesting about a and b
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  18. #17  
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    I don't see anything noticeable about b and c or a and b. The only thing you know about b and c is that their sum has to be 80.
    Quote Originally Posted by DrRocket
    Quote Originally Posted by Harold14370
    Quote Originally Posted by DrRocket
    I am a bit surprised that you are using degrees exclusively in a mathematics class. Usually angles are treated in radians and the correspondence with degrees is only brought in so that students who encounter degrees in engineering or physics applications later on don't get confused.
    Doc, I'm surprised that you're surprised. I recall using degrees in high school geometry class. Every schmo understands angles in degrees before they ever take a high school math class.
    I'm not surprised that they are using degrees. I am surprised that they are using degrees exclusively.

    I agree that every schmo understands angles in degrees. But I thought the educational process would take geometry students beyond the level of every schmo.

    I have to admit that it has been sufficiently long since I took geometry in high school that I am not positive that we used radians, but I think we did. I am dead certain that by the following year we were using radians as a matter of course. It has been a long time, but I think that as soon as I understood what a right angle was I also knew that the angle was .

    I don't remember ever using degrees rather than radians in physics or electrical engineering classes. When I taught trigonometry I taught both radians and degrees and used whichever was most convenient at the time -- degrees are easier when you have to do table look-ups. I don't recall ever using degrees exclusively.
    I guess it depends on where you studied. Basic geometry was in degrees. It's only when you start doing goniometric calculations and using Taylor expansions and such that you need radians.
    About the engineering thing: we use degrees in basic geometrical problems, and radians for everything else. The reason? Probably because we've always learned to calculate basic geometries with degrees. I'm still more comfortable with degrees. e.g. I can easily imagine an angle of 10 or 270, but 0.1745 or 4.7124 don't really mean a thing to me.
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  19. #18  
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    I just thought it was interesting that the small angles for B & C could be any number so long as the both added up to 40. So b could be 1 and c 39, making B 2 and C 78 and A 100. Thats all I was getting at, I don't know a lot about geometry and triangles and we never talked about that during class so I just tought it was interesting.
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