Calculus problem dealing with sun/shadows?

Question

The angle of the sun [overhead] increases @ a rate of 0.25 rad/hr. When the sun is only pi/36rad above the horizon at sunrise, how many feet per minute is the length of a shadow increasing, if the person is 2 meters tall?

Thank you so much for your insight.

Answer 1

2π/24 = 0.2618, but 0.25 is a close approximation.
tanθ = h/s
s = h/tanθ
ds/dt = (ds/dθ)(dθ/dt)
ds/dθ = (0 - hsec^2θ)/tan^2θ
ds/dθ = (-h/cos^2θ)(cos^2θ/sin^2θ)
ds/dt = (-h/sin^2θ)(dθ/dt)
ds/dt = -(2 m)(3.28 ft/m)(0.25 rad/hr)(1 hr/60 min)/sin^2(π/36)
ds/dt = -11,783 ft/min