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Math Help - how to find the third vertex

  1. #1
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    Unhappy how to find the third vertex

    Known two vertices A(x1,y1) and B(x2,y2) of a triangle, how to find the third vertex C(x3,y3)? Also known the length of AB as a units and angle B = alpha degrees.

    Well i wud like to know the general method(which include only variables) to find the third vertex, So that i can get the result just by applying the formula.

    The only unknowns angle A,angle C,length of BC and length of CA.

    I tried to figure it out assuming that a cirlce that passes thru these three vertices as shown in the attachment..............

    But i cud'nt succeed. Please help me.
    Attached Thumbnails Attached Thumbnails how to find the third vertex-tri.jpg  
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ragsk
    Known two vertices A(x1,y1) and B(x2,y2) of a triangle, how to find the third vertex C(x3,y3)? Also known the length of AB as a units and angle B = alpha degrees.

    Well i wud like to know the general method(which include only variables) to find the third vertex, So that i can get the result just by applying the formula.

    The only unknowns angle A,angle C,length of BC and length of CA.

    I tried to figure it out assuming that a cirlce that passes thru these three vertices as shown in the attachment..............

    But i cud'nt succeed. Please help me.
    You will not succeed, because the constraints are not enough to pin the vertex C in one fixed place.
    Per the givens, point C is free to be anywhere on that ray (BC) of the known angle B---as long as point C does not coincide with point B.

    If C is close to B, angle A will be small. As C goes away from B, the angle A becomes bigger. There are infinitely many answers as per the givens.

    If the circle that you thought of has a known dimension---radius, diameter, circumference, coordinates of the center,....---then there will be only one answer. If the circle has no known dimension, then there are infinitely many answers.
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