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Math Help - differential question

  1. #1
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    Question differential question

    Hi,
    The sides of triangle ABC are correctly measured but there is an error of $h^o$ in the measurement of angle A.Show that the error in calculating the area of triangle is approximately (1/2)h b c cos A, in the usual notation.


    Now, here I know the law of cosine and area of triangle also. But some hint to solve this question is needed?
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  2. #2
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    Re: differential question

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  3. #3
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    Re: differential question

    Hello, Vinod!

    The sides of triangle ABC are correctly measured but there is an error of $h$ radians in the measurement of angle A.
    Show that the error in calculating the area of triangle is approximately (1/2)h b c cos A, in the usual notation.

    The area of a triangle is given by: . X \:=\:\tfrac{1}{2}bc\!\cdot\!\sin A

    Take differentials: . dX \;\approx\;\tfrac{1}{2}bc\!\cdot\!\cos A\!\cdot\!dA
    . . . . . . . . . . . . . . . \uparrow \qquad\qquad\qquad\;\;\;  \uparrow
    . . . . . . . . . . . . \text{Area error} \qquad\quad \text{Angle error}


    Therefore: . dX \;\approx\;\tfrac{1}{2}bc\!\cdot\!\cos A\!\cdot\!h
    Thanks from Vinod
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  4. #4
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    Re: differential question

    Hello, Soroban,
    This was easy question. I was just thinking for other form for area of triangle formula, in the meanwhile, I received your reply with answer. Any way, thanks for your reply with correct answer.
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