SOLUTION: a girl flies a kite at a height of 310ft. the wind carries the kite horizontally away from her at a rate of 26fps. How fast must she let out the string when the kite is 530ft away

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Question 1116267: a girl flies a kite at a height of 310ft. the wind carries the kite horizontally away from her at a rate of 26fps. How fast must she let out the string when the kite is 530ft away from her.
Answer by Alan3354(69443) About Me  (Show Source):
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a girl flies a kite at a height of 310ft. the wind carries the kite horizontally away from her at a rate of 26fps. How fast must she let out the string when the kite is 530ft away from her.
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It's a right triangle.
c = hypotenuse = 530 ft
310 = side a
horizontal distance = side b
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c^2 = a^2 + b^2 = b^2 + 310^2
2c*dc/dt = 2b*db/dt
2c*dc/dt = 2b*26 = 52b
dc/dt = 52*429.884/(2*530)
dc/dt =~ 21.09 ft/sec
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Or:
Angle with the ground at the girl = asin(310/530) =~ 35.796º = angle A
26*cos(A) = 21.09 ft/sec