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Thread: Using Pythagorean theorem twice

  1. #1
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    Using Pythagorean theorem twice

    There is a problem I don't know how to solve, only that you are going to use the Pythagorean theorem twice.

    From a house, there are two small roads to a bigger main road. The two roads are 1 and 2 km. The distance along the main road between the two road's connections with it is 1.5 km. You want to plan for a new road from the main road to the house. You want the new road to become as short as possible. How long will this road be?

    Answer: 0,97 km
    Last edited by EulerWannabe; Mar 25th 2017 at 12:57 AM.
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  2. #2
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    Re: Using Pythagorean theorem twice

    Hey EulerWannabe.

    Have you tried drawing a diagram?
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  3. #3
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    Re: Using Pythagorean theorem twice

    HINT:
    new road hits main road at 90 degrees angle
    this will "create" 2 right triangles
    use Big Pete Pythagoras' formula on both

    Given answer is correct: .9682458....
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  4. #4
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    Re: Using Pythagorean theorem twice

    Two right triangles ... two equations

    $x^2+y^2=1^2$

    $(x+1.5)^2 + y^2 = 2^2$
    Attached Thumbnails Attached Thumbnails Using Pythagorean theorem twice-road_prob.png  
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  5. #5
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    Re: Using Pythagorean theorem twice

    The posts above show you the mechanics.

    But to realize why those are the correct mechanics, you have to remember that the shortest distance between a line and a point not on that line is measured along a line that includes the given point and is perpendicular to the given line.
    Thanks from Plato
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  6. #6
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    Re: Using Pythagorean theorem twice

    Thank you so much and sorry for not giving you more information on what I had done before. I did already draw a diagram but I tried to solve it with only one variable. Ended up with the the following fantastic equality: 4 = 4. Not very exciting. xD
    Thanks again!
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