In triangle $ABC$, $AB$ is $3$ cm and $AC$ is $2$ cm and angle $BAC$ is increasing at a

Question

In triangle $ABC$, $AB$ is $3$ cm and $AC$ is $2$ cm and angle $BAC$ is increasing at a constant rate of $0.1$ rad/s. Let angle $BAC = \theta$. Express $BC$ in terms of $\theta$. Find the rate of change of $BC$ when $\theta = \frac{\pi}{3}$.

Accepted Answer

(i) $BC=\sqrt{13-12\cos\theta}\text{ cm}$ (ii) $\dfrac{3\sqrt3}{10\sqrt7}\text{ cm s}^{-1}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

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