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Related Rates, find d(theta)/dt

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    A plane is approaching an observer from an altitude of 5 mi at a dx/dt of 600 mi/h. Find the d(theta)/dt when theta is 30 degrees, 60 degrees, and 75 degrees.

    2. Relevant equations

    tan(theta) = x/y
    5csc(theta) = r

    3. The attempt at a solution

    For my d(theta)/dt I had the formula of 3000/(5csc(theta))^2

    The answers I had were wrong according to the text.

    Please help.
  2. jcsd
  3. Oct 16, 2008 #2


    Staff: Mentor

    You have too many variables. All you need are two: one for the horizontal distance and one for the angle.

    I presume that y is the altitude of the plane, which is given and is not changing. I'm guessing that r is the length of the hypotenuse of the right triangle. Keep in mind that if x is the horizontal distance, it is decreasing because the plane is approaching the observer, so dx/dt will necessarily be negative.

    I have no idea how you got what you have for d(theta)/dt.
  4. Oct 17, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    All you need is [itex]tan(\theta)= height/distance[/itex]. You are told that the height is always 5 mi and that the distance is decreasing at 600 mi/hr.

    With [itex]\theta= arctan(500/x)[/itex], what is [itex]d\theta/dx[/itex] and from that what is [itex]d\theta/dt[/itex]?
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