A kite 100 ft above the ground moves horizontally at a speed of 12 ft/s. At what rate is the angle (in radians) between the string and the h?

Refer to the diagram below.

In ΔABC:
tan28° = h/(x + 100)
h/tan28° = x + 100 …… [1]

Refer to the diagram below.

When s = 200:
x² = s² - 100² (Pythagorean theorem)
x = √(200² - 100³)
x = 100√3

cotθ = x/100
θ = tan⁻¹(0.01x)
dθ/dt = {-0.01/[1 + (0.01x)²]} (dx/dt)

When dx/dt =12 and x = 100√3:
dθ/dt = {-0.01/[1 + (0.01*100√3)²]} * 12
dθ/dt = -0.03

The rate of the angle = -0.03 radian/s
(the "-" sign means that the angle is decreasing.)