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.
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.
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.)