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Math Help - proof: triangle of variable length on the Cartesian plane

  1. #1
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    proof: triangle of variable length on the Cartesian plane

    A variable triangle OAB is formed by a straight line passing through the point P(a, b) on the Cartesian plane and cutting through the x-axis and y-axis at A and B respectively.
    If the angle OAB=theta, find the area of triangle OAB in terms of a, b, and theta.
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  2. #2
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    Quote Originally Posted by shawli View Post
    A variable triangle OAB is formed by a straight line passing through the point P(a, b) on the Cartesian plane and cutting through the x-axis and y-axis at A and B respectively.
    If the angle OAB=theta, find the area of triangle OAB in terms of a, b, and theta.
    Hello Shawli:

    grad =tan(\theta)

    tan(\theta)=\frac{b-B}{a}

    b-a.tan(\theta)=B

    tan(\theta)=\frac{b}{a-A}

    \frac{a.tan(\theta)-b}{tan(\theta)}=A

    Area=\frac{1}{2}.A.B (Substitute the values of A & B)

    Hope this helps
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  3. #3
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    Name the points 0,c)~\&~Ad,0)" alt="B0,c)~\&~Ad,0)" />.
    Then the area of the triangle is \frac{cd}{2}.
    The slope of the line is -\tan(\theta).
    Use that to find c~\&~d.
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