Rate of change

Since tanθ = 20/x where x is the distance between a boat and a lighthouse.

Take derivative on both sides w.r.t to t

(secθ)^2(dθ/dt) = (-20/x^2)(dx/dt)...(1)

when the boat is 50m away from the lighthouse,

secθ = 1/cosθ = √2900/50

Sub. into (1)

(2900/2500)(dθ/dt) = (-20/2500)(-4)

dθ/dt = 5/2900

dθ/dt = 1/580 (radians/s)

2011-01-19 15:14:39 補充：
Sorry, (2900/2500)(dθ/dt) = (-20/2500)(-4)

dθ/dt = 80/2900

dθ/dt = 4/145 (radians/s)

Why we have to sub. dx/dt = -4 instead of 4?