related rates issue

[spezialize]

A kite 100ft above the ground moves horizontally at a speed of 8ft/s. At what rate is the angle between the string and the horizontal decreasing when 200ft of string have been let out..

Alright I know that I think I need to use a triangle and the pyth. thereom. hwoeever i am unsure how to set this up and go about it espec. with the implic. diff

 

[stapel]

Draw the right triangle, with the kite's string source to the left, the vertical height labelled as "y = 100, dy/dt = 0", the horizontal distance (at the top end of the vertical-height line) labelled as "x, dx/dt = 8", and the diagonal line (the hypotenuse) labelled as "s = 200".

Use the Pythagorean Theorem to find the numerical value of x, for the given values of y and s.

Draw the other right triangle, along the ground, that completes the rectangle of length x and height y. Note that the angle ß ("beta", along the ground, at the string source) is the angle that they're asking about. Label this triangle similarly to the other.

You are asked for dß/dt. Note that tan(ß) = y/x. Differentiate implicitly with respect to time t, and use the known values of x, y, dx/dt, and dy/dt.

Eliz.