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Math Help - Trig angle problem

  1. #1
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    Trig angle problem

    If anyone can help me solve this problem it would be greatly appreciated. I have been looking at it all day and cant for the life of me work out how to do it (it may not even be possible with only the variables I have)

    I am trying to calcuate the angle 'Y'. I have labeled everything that I know.

    I am pretty sure the answer is going to be pretty complicated. Feel free to ask any questions to anything that may not be clear.
    Attached Thumbnails Attached Thumbnails Trig angle problem-trig_problem.jpg  
    Last edited by Diessence; September 6th 2009 at 03:14 PM. Reason: Modified picture to show length F and conbined X' & X'' to one angle
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  2. #2
    Senior Member pacman's Avatar
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    i can not understand your sketch, where is the original problem? In this forum we have a company of math helpers, please provide additional information . . . . thanks
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  3. #3
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    Quote Originally Posted by Diessence View Post
    If anyone can help me solve this problem it would be greatly appreciated. I have been looking at it all day and cant for the life of me work out how to do it (it may not even be possible with only the variables I have)

    I am trying to calcuate the angle 'Y'. I have labeled everything that I know. The only thing that isnt real clear is that I know what X' + X'' is, i dont know what they are individually.

    I am pretty sure the answer is going to be pretty complicated. Feel free to ask any questions to anything that may not be clear.
    Since  \angle X' &  \angle X'' constrain the location of the square and
    distances d & e (which do not have to be parallel) also constrain the placement of the square
     \angle Y it will have a unique solution.
    Last edited by aidan; September 2nd 2009 at 08:19 AM. Reason: correct a typo
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  4. #4
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    pacman.. what can you not understand about the diagram.. please let me know and i will try and explain it better

    aidan.. are you saying it can or cant be done with what i have given you?

    feel free to make any new shapes, distances, angles (by using the given variables) that you feel may be necessary to find an answer for angle Y
    Last edited by Diessence; September 2nd 2009 at 01:53 PM. Reason: typo
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  5. #5
    Senior Member pacman's Avatar
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    I cannot figure out what to do with it, a closer look with it, your triangle ABC is a 45-45-90 triangle, and your angle y is also 45 degrees, by visual interpolation, it is 45 degrees. did you draw it to scale?
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  6. #6
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    Quote Originally Posted by Diessence View Post
    If anyone can help me solve this problem it would be greatly appreciated. I have been looking at it all day and cant for the life of me work out how to do it (it may not even be possible with only the variables I have)

    I am trying to calcuate the angle 'Y'. I have labeled everything that I know. The only thing that isnt real clear is that I know what X' + X'' is, i dont know what they are individually.

    I am pretty sure the answer is going to be pretty complicated. Feel free to ask any questions to anything that may not be clear.
    see attached sketch for clarity

    Two Solutions.
    1) Line e is parallel to line d
    2) Line e is NOT parallel to line d

    SOLUTION 1:
    Line e IS PARALLEL TO Line d

    f'= \dfrac{(c")^2 - a^2 + (d-e)^2}{2(d-e)}

     <br />
f" = \sqrt{ (c")^2 + (f')^2 }<br />

     <br />
\angle z' = arctan \left ( \dfrac{f"}{f'} \right )<br />

     <br />
\angle z" = arctan \left ( \dfrac{ d -e -f'}{f"} \right ) + 90deg<br />

     <br />
\angle v' = 270deg - \angle z"<br />

     <br />
\angle v" = 360deg - (x'+z'+v')<br />

     <br />
\angle w = 270deg - v"<br />

     <br />
\angle y = 180deg - ( \angle w + \angle x)<br />
    Attached Thumbnails Attached Thumbnails Trig angle problem-mhftri0001.jpg  
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  7. #7
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    pacman: the angle X' + X'' does not have any real value associated with it. In real life it could be anywhere from 30-50 degrees. I am after a solution for angle Y that is formulas only. That way once I put it into a real life situation a can calcuate Y for any situation.

    aidan: You solution looks good, except for when you calcuated V'' you used X' in the solution. Remember, I only know what X'+X'' is, I dont what what they are individually. Also, we cant assume that e and d are going to be parallel.
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  8. #8
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    [quote=Diessence;358971]
    aidan: You solution looks good, except for when you calcuated V'' you used X' in the solution. Remember, I only know what X'+X'' is, I dont what what they are individually.[quote]
    Then you should NOT have given both of them. You should have given only 1 value.
    You need to correct your drawing.


    Also, we cant assume that e and d are going to be parallel
    from my 2nd post:
    Two Solutions.
    1) Line e is parallel to line d
    2) Line e is NOT parallel to line d
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  9. #9
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    Aidan: I didn't know how to draw showing that full angle with only one label. I will red0 my drawing.. also I have just realised I have forgotten to label a line I know. Length F is known. Sorry.

    Aidan: I can not see you "Solution 2". Are you saying that the above equations will work for any case?
    Attached Thumbnails Attached Thumbnails Trig angle problem-trig_problem.jpg  
    Last edited by Diessence; September 7th 2009 at 03:57 PM.
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