An isosceles triangle has equal sides of length 12m. If the angle theta between these sides is increased from 30 to 33 degrees, use differentials to approximate the change in the area of the triangle.

Any help would be very much appreciated.

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- Feb 22nd 2013, 01:05 PMJtgs5249Solve the area of an isosceles triangle with differentials
An isosceles triangle has equal sides of length 12m. If the angle theta between these sides is increased from 30 to 33 degrees, use differentials to approximate the change in the area of the triangle.

Any help would be very much appreciated. - Feb 22nd 2013, 02:46 PMBobPRe: Solve the area of an isosceles triangle with differentials
The area of the triangle will be given by $\displaystyle A=\frac{1}{2}12^{2}\sin \theta$, where intially $\displaystyle \theta=30$ degrees.

If $\displaystyle \theta$ is increased by some small ammount $\displaystyle \delta \theta,$ the increase in area $\displaystyle \delta A $ will be given (approximately) by

$\displaystyle \delta A \approx \frac{dA}{d\theta}\delta \theta.$

(Remember that now, $\displaystyle \theta$ should be measured in radians.)