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Math Help - Calculating internal angles of trapezium

  1. #1
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    Calculating internal angles of trapezium

    I have to calcute the internal angles of trapezium when I know all sides of that trapezium. How can I do it? I've tryied to solve it but I can't find any solution to this.
    Here are the sides of the ABCD trapezium: |AB|=73,6; |BC|=57; |CD|=60; |DA|=58,6; AB//CD
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  2. #2
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    Re: Calculating internal angles of trapezium

    Quote Originally Posted by Serillan View Post
    I have to calcute the internal angles of trapezium when I know all sides of that trapezium. How can I do it? I've tryied to solve it but I can't find any solution to this.
    Here are the sides of the ABCD trapezium: |AB|=73,6; |BC|=57; |CD|=60; |DA|=58,6; AB//CD
    1. Draw a sketch.

    2. I'm referring to my labels now:

    x+y=13.6~\implies~y=13.6-x

    h^2+x^2=58.6^2
    h^2+y^2=57^2

    3. Subtract the last 2 equations. You'll get:

    x^2-y^2=58.6^2-57^2

    Replace y by 13.6 - x. You'll get an equation in x.

    4. You should com out by x = 13.6 and y = 0.

    5. Now use the right triangle at the left to determine the missing angles.
    Attached Thumbnails Attached Thumbnails Calculating internal angles of trapezium-trapezstrecken.png  
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: Calculating internal angles of trapezium

    If you drop a line from point D that is perpendiclar to AB, and call the intersection point with line AB 'E'. Let x = the distance from E to B. Do the same with a line from point B to the line CD, and call that intersection point F, and the distance from F to D is also x . From pythagoras you have the height of the figure is:

    58.6^2 - (73.6-x)^2

    which also equals  57^2-(60-x)^2

    From this you can solve for x, and then apply standard trig functions to find the angles.

    Calculating internal angles of trapezium-trapezoid.jpg
    Attached Thumbnails Attached Thumbnails Calculating internal angles of trapezium-trapezoid.jpg  
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