Calculus Related Rates Problem

Question

A kite  above the ground moves horizontally at a speed of . At what rate is the angle (in radians) between the string and the horizontal decreasing when  of string have been let out?

I got -1.9 and i dont know why i am wrong can someone show the work and answer please. Thank you so much.

Answer 1

i² = x² + h²; We differentiate this by time t: 2ldl/dt = 2xdx/dt; But l = hcscθ; dl/dt = -hcscθcotθdθ/dt;

-lhcscθcotθdθ/dt = xdx/dt; cscθ = 200/100 = 2; cotθ = 100√3/100 = √3; x = 100√3; dx/dt = 9m/s

-200·100√3·2dθ/dt· = 100√3 ·9; dθ/dt = - 900/40000 = - 0.0225 rad/s