# Rate of change of the area of a triangle

Calculus Level 3

In triangle $$\text{ABC}$$ above, $$\overline{\text{AB}}=2$$ and $$\overline{\text{BC}}+\overline{\text{CA}}=2\overline{\text{AB}}.$$ Let $$\angle \text{B}=\theta$$ and suppose that the rate of change of the angle $$\theta$$ with respect to time is $$\displaystyle \frac{d\theta}{dt}=2(\text{rad/sec}).$$ Then, if $$S$$ is the area of the triangle, what is the the rate of change of $$S$$ with respect to time when $$\displaystyle \angle \text{A}=\frac{\pi}{2}?$$

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