Question

The included angle of the two sides of constant equal length s of an isosceles triangle is θ.

A=(1/2)*(s^2)*sinθ

If θ is increasing at the rate of (1/8) radian per minute, find the rate of change of the area when θ = pi/3.

Thank you, your help is really appreciated! :)

Answer 1

We just differentiate both sides with respect to t to get
dA/dt=(1/2)(s^2)*cos(θ)dθ/dt

Note that s is constant, so we don't need to differentiate it.

We know that dθ/dt=1/8 rad/min whenθ=π/3

Plugging it into our equation gives

dA/dt=(1/2)(s^2)*cos(π/3)*(1/8)=0.03125*s^2

We cannot find s because we are only given the angle.

Thus the above is the solution.