Rate of change of the area of a triangle

Calculus Level 4

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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