the area of a triangle with sides of length a and b and contained angle θ is A=(1/2)absinθ

Question

the area of a triangle with sides of length a and b and contained angle θ is A=(1/2)absinθ

 

(a)if a=2cm, b=3cm, and θ increases at a rate of 0.2 rad/min, how fast is the area increasing when θ=π/3?

 

theres few set up like this but i couldn't find a quality example in my book so i just need help with this one to do the rest.

Answer 1

A = 1/2 a b sin T

 

dA= 1/2 a b cos T dT

 

   = 1/2 *2*3* cos(pi/3)*.2

= 0.3