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Homework Help: Another GRE questions

  1. Mar 13, 2010 #1
    What is the greatest possible area of a triangular region with one vertex at the center of radius 1 and the other two vertices on the circle?

    What is the best way to maximize the area of a triangle in this instance?
     
  2. jcsd
  3. Mar 13, 2010 #2

    LCKurtz

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    Put one vertex at (1,0), the second around at angle θ, calculate the corresponding area and maximize it as a function of θ.
     
  4. Mar 13, 2010 #3
    The area of a triangle inscribed in circle is 1/2 * (AB)[tex]^{2}[/tex] * sin(theta), correct? A 90 degree angle is going to yield maximum multiple of AB; however, is a lesser or greater angle with a longer length going to increase the area more?
     
  5. Mar 13, 2010 #4

    LCKurtz

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    What are A and B? The only variable in the problem is θ. And, no, that is not the correct formula for a triangle with sides A and B and included angle θ.
     
  6. Mar 13, 2010 #5
    Then what is the formula for the area of a triangle using an angle theta?
     
  7. Mar 13, 2010 #6
    The answer is 1/2, right?
     
  8. Mar 13, 2010 #7

    LCKurtz

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    You are reviewing for the GRE and you can't figure that out?? Draw a little triangle with sides A and B, included angle θ and height h and figure out its area.
     
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