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Math Help - Finding the apex - Simple Trig, but can't figure it out.

  1. #1
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    Finding the apex - Simple Trig, but can't figure it out.

    Finding the apex - Simple Trig, but can't figure it out.-apex.jpg

    In the above drawing, it is simple to find the angles and legs of each individual triangle using Trig. For example, the one angle is = ATan(((3.0 - 2.5)/2)/2.1).

    The other angle is, = ATan((((3.0 - 2.6)/2)/(1.6 - 0.9)).

    Using those angles, I can find the hypotenuse of either triangle. However, in order to find "X" in this drawing, it is dependant on BOTH angles, and not just one.

    Usually in Trig, all I need is one angle and one side, or 2 sides.....but when something like this, which involves 2 angles....I'm stumped!!!

    Does anyone know how to solve this?

    Thanks a lot!
    Last edited by bkelly301; October 13th 2010 at 12:04 PM. Reason: Solved!
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  2. #2
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    Quote Originally Posted by bkelly301 View Post
    Click image for larger version. 

Name:	apex.jpg 
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    In the above drawing, it is simple to find the angles and legs of each individual triangle using Trig. For example, the one angle is = ATan(((3.0 - 2.5)/2)/2.1).

    The other angle is, = ATan((((3.0 - 2.6)/2)/(1.6 - 0.9)).

    Using those angles, I can find the hypotenuse of either triangle. However, in order to find "X" in this drawing, it is dependant on BOTH angles, and not just one.

    Usually in Trig, all I need is one angle and one side, or 2 sides.....but when something like this, which involves 2 angles....I'm stumped!!!

    Does anyone know how to solve this?

    Thanks a lot!
    I can show you a way to solve this question, but I don't use trigonometry.

    1. I define a coordinate system. The axes are drawn in blue.

    2. At the left side of the image you can determine 4 points by their coordinates:

    A(0, 2.5), B(0.25, 0.4). Then the straight line through A and B has the equation:

    y-2.5 = \dfrac{-2.1}{0.25} \cdot x~\implies~y=-8.4x+2.5

    C(0, 0), D(0.2, 1.6). Then the straight line Through C and D has the equation:

    y = \dfrac{1.6}{0.2} \cdot x ~\implies~y=8x

    3. Calculate the coordinates of the point of intersection. You'll get I\left(\frac{25}{164} \ ,\ \frac{50}{41}\right)

    4. Do the same at the right side of the image with the points A', B', C', D' and I'.
    Calculate the length X=|\overline{II'}|. I didn't label the points!

    5. I've got |\overline{II'}| =X= \dfrac{221}{82}
    Attached Thumbnails Attached Thumbnails Finding the apex - Simple Trig, but can't figure it out.-mittparallaenge.png  
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  3. #3
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    Wow, I would have never thought about doing it that way. Thanks a lot! At my job, I use trig all the time, but I haven't used basic y=mx + b algebra since I was in school, so I forgot all about that.

    The whole point of this is that I want to make up a little excel program where I plug in all the given values (all the numbers shown), and it outputs what X will be. Now that I know how to solve this problem mathematically, I can figure out how to put it into an excel program.

    Much appreciated. Thanks again!
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