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A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 5 ft from the wall? Evaluate your answer numerically. (Round the answer to three decimal places.)

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    let x be the horizontal distance from wall to ladder.

    cosineTheta=x/10

    10 cosTheta=x

    -10sinTheta dTheta/dt= dx/dt

    so you are looking for dTheta/dt

    when x=5, theta = arccos.5, or 60 deg, and sin of 50 = .877

    dTheta/dt= dx/dt / (10*.877)

    check all that.

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    .228

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