# Thread: [SOLVED] Triangulation

1. ## [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.

1. Radius:
• $\displaystyle r_{S1}=100\sqrt{10} mi$
• $\displaystyle r_{S2}=200 mi$
• $\displaystyle r_{S3}=100\sqrt{13} mi$

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

3. Finding epic center by setting the equations equal:
• $\displaystyle y_{S1}=\pm\sqrt{r_{S1}^2-(x+100)^2}-200$
• $\displaystyle y_{S2}=\pm\sqrt{r_{S2}^2-(x+400)^2}-500$
• Set $\displaystyle y_{S1}=y_{S2}$, 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 $\displaystyle y_{S3}=y_{S1}$, or set $\displaystyle y_{S3}=y_{S2}$. 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.