The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is $\theta= 60°$, is :
Answer & explanation
Correct answer: option 1
x = 10 cm
y = 12 cm
θ = 60°
x, y → constant
θ → variable using concept of vectors
|Area| = $\frac{xy \sin \theta}{2}$ (magnitude of area)
so $\frac{d A}{d \theta}=\frac{x y \cos \theta}{2}=\frac{10 \times 12 \times \cos 60}{2}$
$\Rightarrow \frac{10 \times 12}{2} \times \frac{1}{2}=\frac{30 ~cm^2}{rad}$