# A relative rates calculus problem regarding a kite.

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?

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Trig:

sin(theta) = h/L

cos(theta) = x/L

tan(theta) = h/x

We want x in the equation and h is constant so I would lean towards the

last one. It will be easier if we take the reciprocal and get the cotangent.

cot(theta) = x/h

Being calculus, we have to take the derivative with respect to time:

-(1/sin^2(theta)) theta' = x'/h

using chain rule because theta depends on ...