Calculus Question

Question

A Kite 60 feet above the ground moves horizontally at a speed of 5 ft/s. At what rate is the angle between the string and the ground decreasing when 180 feet of string is out?

Answer 1

x = 60cotθ; dx/dt = - 60csc²θdθ/dt; dθ/dt = - dx/dt·sin²θ/60 = - 5ft/s·(60/180)²/60ft = - 0.00926 rad/s