Calculus word problem

Question

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/sec. At what rate is the angle between the string and the horizontal decreasing when the angle is θ = π 6 radians? Hint: Use a trigonometric function t

Answer 1

x = 100cotθ; dx/dt = - 100csc²θdθ/dt; so dθ/dt = - 0.01sin²θdx/dt = - 0.01sin²π/6·8 = - 0.02 rad/sec

Answer 2

The problem depends on whether you fix the string length at 100 ft, or the height at 100 ft. I solved both for you