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Math Help - Finding the length of segment

  1. #1
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    Finding the length of segment

    This one has been eating at me for a long time and I just can't figure it out:

    In the figure below, ACDF is a parallelogram. Segment AE is perpendicular to line CD, and segment DB is perpendicular to line AC. The length of DB is 6 meters, segment FA is 9 meters and segment AC is 15 meters. How many meters long is segment AE?

    How do I show/prove that it's 10 meters?
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  2. #2
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    Quote Originally Posted by harold View Post
    This one has been eating at me for a long time and I just can't figure it out:

    In the figure below, ACDF is a parallelogram. Segment AE is perpendicular to line CD, and segment DB is perpendicular to line AC. The length of DB is 6 meters, segment FA is 9 meters and segment AC is 15 meters. How many meters long is segment AE?

    How do I show/prove that it's 10 meters?
    1. Calculate the sinus of the angle at C in the right triangle BCD:

    \sin(C)=\frac69

    2. Calculate the sinus of the angle at C in the right triangle ACE:

    \sin(C)=\frac69=\frac{\overline{AE}}{AC}

    3. Plug in all values you know: AC = 15, sin(C) to calculate

    |\overline{AE}| = \frac69 \cdot 15 = 10
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  3. #3
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    Thanks so much earboth--it was driving me crazy!!
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  4. #4
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    Alternatively, you could recognize the similar triangles, so therefore

    (9/15) = (6/x), thus x=10
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