1. ## 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?

2. ## Re: differential question

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3. ## 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: .$\displaystyle X \:=\:\tfrac{1}{2}bc\!\cdot\!\sin A$

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

Therefore: .$\displaystyle dX \;\approx\;\tfrac{1}{2}bc\!\cdot\!\cos A\!\cdot\!h$

4. ## Re: differential question

Hello, Soroban,