## differentiation problem

hi, could anyone guide as to how to go about solving this question?
[B]A cicular patch of grass or radius 20m is surrounded by a walkway and a light is placed atop a lamppost at the circle's center. At what height shoud the light be placed to illuminate the walkway most strongly? The intensity of illumination "I" of a surface is given by
I = [k.sin(theta)] / D^2 where is the distance from the light source to the surface and theta is the angle at which light strikes the surface, and k i s a positive constant [B]

pls anyone, just give me a push, i am competely cluess as to where to begin.
thanks!
Monsurat.

 PhysOrg.com science news on PhysOrg.com >> 'Whodunnit' of Irish potato famine solved>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change>> Curiosity Mars rover drills second rock target
 Recognitions: Homework Help Science Advisor Just write $\sin \theta$ in terms of D and R (radius of the circle) and set the derivative of I with respect to D equal to 0, etc.
 $$\textrm{Here goes some hints...}$$ $$R = 20 \textrm{ m}$$ $$\hline$$ $$R = D \cos \theta$$ $$h = D \sin \theta = \frac{R}{\cos \theta} \cdot \sin \theta = R \tan \theta$$ $$\hline$$ $$I = k\cdot \frac{\sin \theta}{D^2}$$ $$\sin \theta = \frac{ID^2}{k}$$ $$\frac{h}{D} = \frac{ID^2}{k}$$ $$h = \frac{ID^3}{k}$$ $$h = \frac{I}{k}\left( \frac{R}{\cos \theta} \right)^3$$ $$\textrm{Good luck!}$$