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Math Help - [SOLVED] Triangulation

  1. #1
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    [SOLVED] Triangulation

    S1 is located at (100,200). It's distance to the epicenter is 100 √ 10 miles
    S2 is located at (400,500). It's distance to the epicenter is 200 miles
    S3 is located at (700,100). It's distance to the epicenter is 100 √ 13 miles

    1)What is the radius of S1? S2? S3?

    2)State the equations, in standard form, for circles S1, S2, S3.

    3)State the distance from the base (0,0) to the epicenter?

    Please help me.
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  2. #2
    Junior Member
    Joined
    Feb 2009
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    1. Radius:
      • r_{S1}=100\sqrt{10} mi
      • r_{S2}=200 mi
      • r_{S3}=100\sqrt{13} mi

    2. Equation of circles:
      • S1: (x+100)^2+(y+200)^2=r_{S1}^2
      • S2: (x+400)^2+(y+500)^2=r_{S2}^2
      • S3: (x+700)^2+(y+100)^2=r_{S3}^2

    3. Finding epic center by setting the equations equal:
      • y_{S1}=\pm\sqrt{r_{S1}^2-(x+100)^2}-200
      • y_{S2}=\pm\sqrt{r_{S2}^2-(x+400)^2}-500
      • Set y_{S1}=y_{S2}, you should find these 2 circles intersects at 2 points.
      • There are two way to pick which point is the epic center:
        1. Plug the points into to the third circle and see which one work.
        2. Set y_{S3}=y_{S1}, or set y_{S3}=y_{S2}. Once again you will get 2 points. Only one will be the same as one of the points found previously. That is the point you want.


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