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Derivatives of Trig with Triangles

  1. Dec 30, 2007 #1
    [SOLVED] Derivatives of Trig with Triangles

    1. Two sides of a triangle are six and eight metres in length. If the angle between them decreases at the rate of 0.035 rad/s, find the rate at which the area is decreasing when the angle between the sides of fixed length is pi/6. Answer 0.727 m^2/min


    2. I tried using Heron's formula but I realised it was almost impossible to take the derivative somehoe with the angle needed. My givens are
    dtheta/dt = -0.035 rad/s
    the angle between them is pi/6 or 30 degrees
    Now to find da/dt...


    Thanks
     
  2. jcsd
  3. Dec 30, 2007 #2
    I'm not sure why you're using Heron's formula - that looks to be better when you know all three sides and don't necessarily know any of the angles.

    Can you express the area as a function of the two fixed lengths and the contained angle? It's pretty simple to take the derivative of the relevant expression.
     
  4. Dec 30, 2007 #3
    no sry i don't understand how to express the equation but what i think is cut the triangle into two?
     
  5. Dec 30, 2007 #4
    nvmi got it thank you very much! =) But one thing when u take the derivative of 24sin theta,w hy is it that u leave the 24?
     
  6. Dec 30, 2007 #5
    I'm not sure I understand your question. It's just:

    d/dt (k*f(t)) = k* df/dt , k = constant

    Is that clear?
     
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