Step-by-step explanation:
Area of triangle is with side a and b and angle C between them is given by
A = 0.5 ab SinC
Here we need to find how area changes with a and b fixed and C is changing,
[tex]\frac{dA}{dt}=\frac{d}{dt}\left (0.5 absinC\right )\\\\\frac{dA}{dt}=0.5ab\frac{d}{dt}\left (sinC\right )\\\\\frac{dA}{dt}=0.5abcosC\frac{dC}{dt}[/tex]
We have
a = 8 m
b = 9 m
[tex]C=\frac{\pi}{3}rad\\\\\frac{dC}{dt}=0.06rad/s[/tex]
Substituting
[tex]\frac{dA}{dt}=0.5\times 8\times 9\times cos\left ( \frac{\pi}{3}\right )\times 0.06\\\\\frac{dA}{dt}=1.08m^2/s[/tex]
Rate at which area is increasing is 1.08 m²/s.
