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# A relative rates calculus problem regarding a kite.

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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?

https://brainmass.com/math/calculus-and-analysis/a-relative-rates-calculus-problem-regarding-a-kite-1767

#### Solution Preview

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 = ...

#### Solution Summary

This shows how to find the rate of change of angle of a flying kite.

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