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Math Help - triangles are evil!

  1. #1
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    triangles are evil!

    How many ways are there to find the area of a triangle with coordinates of (-11,0),(0,7),(15,-13)
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  2. #2
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    Quote Originally Posted by extreme_pi
    How many ways are there to find the area of a triangle with coordinates of (-11,0),(0,7),(15,-13)
    Plenty. I do not have all the time now because my attention is on the Super Bowl XL (it's halftime now, my team, Steelers, leading 7 to 3. Zeez, we are just lucky. Our quarterback is nervous. But I see that when the 2nd half resumes, he will explode, meaning, wake up, and he'll kill 'em Seahawks. Man!).
    1) Get the lengths of the 3 sides by distance between two points (x1,y1) and (x2,y2) is sqrt[(x2 -x1)^2 +(y2 -y1)^2]. Then use the Heron's formula. One way.

    2) Enclose the triangle by a rectangle. Area of triangle equals area of rectangle minus the areas of the 3 right triangles enclosing the said triangle. Way #2.

    3) Get the 3 altitudes. Then area = (1/2)(altitude)(base). Ways #3,4,5.

    4) Get the 3 interior angles. Then area = (1/2)(side)(another side)*sin(included angle). Ways #6,7,8.

    5)Get the inradius. Then area = (1/2)(inradius)(perimeter of triangle). Way #10.

    6) Then there is one formula using the circumradius. Way #11.

    Many more, maybe, but cannot concentrate on them now....

    The Living Deads (aka The Rolling Stones) just finished spooking the festivities. Second Half of the Game coming up. See ya later...
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  3. #3
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    Quote Originally Posted by extreme_pi
    How many ways are there to find the area of a triangle with coordinates of (-11,0),(0,7),(15,-13)
    You can use Heron's Formula, if the semiperimeter of a triangle is s
    having sides, a,b,c
    Then its area is,
    A=\sqrt{s(s-a)(s-b)(s-c)}

    Now to find the length of the sides of the triangle you can use the distance formula. It states that the distance between points (x_0,y_0)
    and (x_1,y_1) is:
    d=\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}
    And it does not matter which one is which.

    Here is a picture.
    Attached Thumbnails Attached Thumbnails triangles are evil!-graph2.gif  
    Last edited by ThePerfectHacker; February 5th 2006 at 05:05 PM.
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  4. #4
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    Quote Originally Posted by ticbol
    Plenty. I do not have all the time now because my attention is on the Super Bowl XL (it's halftime now, my team, Steelers, leading 7 to 3. Zeez, we are just lucky. Our quarterback is nervous. But I see that when the 2nd half resumes, he will explode, meaning, wake up, and he'll kill 'em Seahawks. Man!).
    1) Get the lengths of the 3 sides by distance between two points (x1,y1) and (x2,y2) is sqrt[(x2 -x1)^2 +(y2 -y1)^2]. Then use the Heron's formula. One way.

    2) Enclose the triangle by a rectangle. Area of triangle equals area of rectangle minus the areas of the 3 right triangles enclosing the said triangle. Way #2.

    3) Get the 3 altitudes. Then area = (1/2)(altitude)(base). Ways #3,4,5.

    4) Get the 3 interior angles. Then area = (1/2)(side)(another side)*sin(included angle). Ways #6,7,8.

    5)Get the inradius. Then area = (1/2)(inradius)(perimeter of triangle). Way #10.

    6) Then there is one formula using the circumradius. Way #11.

    Many more, maybe, but cannot concentrate on them now....

    The Living Deads (aka The Rolling Stones) just finished spooking the festivities. Second Half of the Game coming up. See ya later...
    WOOOOOOOOOOOOO!!!!!!!!
    MAN !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    ZEEZZZZZZZZZZZZZZZZZZ!!!!
    WE GOT IT!!!!!!!!
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  5. #5
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    YEAHHH Steelers win!!!!!!!!!!!!!!!!!!!

    Now I can get on with my actual life!
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  6. #6
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    Quote Originally Posted by extreme_pi
    YEAHHH Steelers win!!!!!!!!!!!!!!!!!!!

    Now I can get on with my actual life!
    Whoa, you are one of us too? Steelers Nation? Man!

    CONGRATULATIONS!

    Search the Web re "Steelers" or "Steelers Nation" and we'd be in heaven for a long, long time.

    ticbol
    {aka Cowher or Ward or Porter or Bettis or Polamalu or Roethlisberger or ..... for a while, from now on.}
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  7. #7
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    Thank you thank you thank you thank you thank you thank you

    Thanks for the image and the formula, ThePerfectHacker. They should help me out, as I am working on the exact same project.

    BTW, I don't care about football very much. I did host a Super Bowl party, but I did it more to show off my Dance Dance Revolution skills than to watch football. The Steelers won. So.
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