The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is , is:

Question

The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is $θ = 60 °$ , is:

Smart Achievers · Accepted Answer

(1)

Ans. $30 {cm}^{2} / radian$

Explanation:

$a = 10 cm,$ $b = 12 cm$

$θ = 60 °$

$A = \frac{1}{2} a b \sin θ$

Differentiating with respect to $θ$ ,

$\frac{d A}{d θ} = \frac{1}{2} a b \cos θ$

$= \frac{1}{2} \times 10 \times 12 \times \cos 60 °$

$= 60 \times \frac{1}{2} = 30 {cm}^{2} / radian$

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