calculus

A ladder 10 ft long rests against a vertical wall. let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/3

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  1. According to you diagram I have

    cos Ø = x/10
    x = 10cosØ
    dx/dØ = -10sinØ

    so when Ø=π/3
    dx/dØ = -10sin π/3
    = -10 (√3/2)

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  2. SinØ = opp/hyp
    opp is x
    hyp is 10

    SinØ = x/10
    10SinØ = x

    Sin (π/3) = 1/2
    10 * 1/2 = 5

    Answer: 5 ft/rad

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