A kite 100ft above the ground moves away horizontally at a speed of 8ft/sec. At what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?
Attached is a picture of a triangle to show the diagram setup.
Drawing picture is always the first step
in these kind of problems.
let x be the horizontal distance traveled, h be the height, L be the length of string let out and theta be the angle.
Next we need to find that something that is always true about our triangle.
Two things spring to mind:
Pythagoras: x^2 + h^2 = ...
This shows how to find the rate of change of angle of a flying kite.