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Thread: dont know which side is base or height

  1. #1
    Nov 2007

    dont know which side is base or height

    I have a triangle located at the points A(-2,5),B(1,3),C(-1,0)

    The distance from point A to B is $\displaystyle \sqrt{13}$.

    The distance from point B to C is $\displaystyle \sqrt{13}$

    The distance from point A to C is $\displaystyle \sqrt{26}$

    The book wants me to find the area of the triangle. But I dont even know what the base or the height of the triangle is. How do I know what the base is and what the height is?

    Edit: I think I may have just figured something out. Are the sides adjacent to the right angle always the base and height? Yeah that seems so obvious now.

    But what about triangles that arent right triangles? How would I go about finding the base and height of those?
    Last edited by mitchelljk; Mar 17th 2009 at 07:36 PM.
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  2. #2
    MHF Contributor
    Mar 2007


    Given that a triangle is right, yes, the lengths of the sides containing the right angle can be used as the "height" and the "base".

    In general, of course, the triangle won't be right. In such a case, plot the points so you can see which side you feel would most-usefully be the "base". This will probably be the side opposite an angle from which you can drop a perpendicular and have that perpendicular intersect the side.

    Find the slope of the line containing the side you've chosen to be the base. Then find the equation of that line.

    Find the perpendicular slope, and then the equation of the perpendicular line passing through the vertex opposite the base. This is the line containing your "height" line.

    Now that you have two line equations, you can solve the system of equations to find the point where the "height" line reaches the "base" line.

    Use the Distance Formula to find the value for the height. Etc, etc, etc.

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