I need help ASAP Calc problem

Question

A girl flies a kite at a height of 280 feet.The wind carries the kite horizontally away from her at a rate of 24 fps. How fast must she let out string when the kite is 480 feet away from her

Answer 1

let c be the distance from the girl to the kite (measured along the string). We need to find dc/dt at the instant when c = 480. We know that da/dt = 24, where a is the distance from the girl to the kite measured horizontally, more precisely, the distance from the girl to the spot on the ground right below the kite. Then a² + 280² = c² , 2a da/dt = 2c dc/dt and when c = 480, a = sqrt(480² - 280² ) = 390 Plug in the values, solve for c dc/dt, get

c dc/dt = (390/480) x 24 = 19.5