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Math Help - Related rates question!!!

  1. #1
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    Related rates question!!!

    Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60?

    in this question i think i need to use the cosines law right..but how can i take the derivatives of the cosines law??
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  2. #2
    Member arpitagarwal82's Avatar
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    cosine law
    a^2 = b^2 + c^2 - 2bc \cos x

    x is angle between b and c

    2a da/dt = 2bc \sin x dx/dt
    da/dt =  (bc \sin x dx/dt)/a
    = (bc \sin x  dx/dt)/ \sqrt ( b^2 + c^2 - 2bc \cos x)

    now substitute the value of b, c dx/dt and x (we have to find da/dt when x = 60 degree)
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