A kite 118 ft above the ground moves horizontally at a speed of 6ft/s. At what rate is the angle between the string and the horizontal decreasing when 236 ft of string have been let out?

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- January 7th 2007, 11:43 AMasnxbbyx113Related Rates
A kite 118 ft above the ground moves horizontally at a speed of 6ft/s. At what rate is the angle between the string and the horizontal decreasing when 236 ft of string have been let out?

- January 7th 2007, 12:42 PMgalactus
We want when dx/dt=6.

The kite's string makes the hypoteneuse of the triangle. When 236 of string

is out then the angle is

at that instant.

Now, using

- January 7th 2007, 01:08 PMSoroban
Hello, asnxbbyx113!

Quote:

A kite 118 ft above the ground moves horizontally at a speed of 6 ft/s.

At what rate is the angle between the string and the horizontal decreasing

when 236 ft of string have been let out?

Code:`x`

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118 | *

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We have: .

Differentiate with respect to time: .

. . And we have: .**[1]**

When the string is feet, Pythagorus gives us:

. .

. . Then: .

. . And we are told that: . ft/sec.

Substitute into**[1]**: . radians/sec