1. The problem statement, all variables and given/known data A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200ft of the string has been let out? 2. Relevant equations - 3. The attempt at a solution I've tried two different methods to come up with the answer but i'm not sure which one is correct. In one case, I've got: cosθ = x/200 And in the other one: tanθ = 100/x However, when I try to derive both sides of both equations in order to get the result, I found out that the values of dθ/dt are actually different for each equation. For example, in the first case: -sinθ (dθ/dt) = 1/200 (dx/dt) Clearing this out makes the final result as (-2/25) On the other hand: sec2 (dθ/dt) = -(dx/dt) / 3 Clearing this out makes the final result as (-1/50) Is there a reason for this incongruity or have I made a mistake in my calculations? Thank you very much guys.