Good Morning,

I would like to better understand the method or methods used to calculate and determine bearing and distance from a known point based on observation(s) from two known points.

Let me explain mo Lets use a 60,60,60 triangle so there is no confustion about what side is the base. I have two observation towers, Tower Left, and Tower Right. and the tip or top is the target. If I observe a bomb/explosion/ect... at a point that is 10 degrees left of the target from the left tower and 10 degrees right of the target from the right tower. I now have a new triangle that is 70,70,40 and I can calculate the leg lengths. where I am lost is trying to determine the bearing & distance from the target to the new spot. using this example it would be due north of the target i.e. 360 or 12 o'clock, but I am not sure how to find distance at this point. any assistance in a medthod or solution would be greatly appreciated. Don

Good morning Don,

Thank you for reaching out for assistance with triangulation using Excel. I can definitely help you with this.

To determine the bearing and distance from the target to the new spot, you will need to use trigonometry. Specifically, you will need to use the law of sines and the law of cosines.

Here are the steps to follow:

1. Calculate the length of the base of the new triangle (the distance between the two observation towers). You can use the law of cosines for this. Let's call this length "b".
2. Calculate the angles at the target. You already know that one angle is 70 degrees. To find the other two angles, you can use the law of sines. Let's call the angle opposite the side of length "b" "A", and the angle opposite the side of length "40" "B". Then:
   
   
   Formula:

   sin(A)/b = sin(70)/60
   sin(B)/40 = sin(70)/60 

   Solve for A and B.
   
3. Calculate the length of the side opposite angle A (the distance from the target to the new spot). You can use the law of sines again:
   
   
   Formula:

   sin(A)/x = sin(70)/40 

   Solve for x.
   
4. To find the bearing, you will need to use the angles you calculated in step 2. The bearing is the angle between due north and the line connecting the target to the new spot. Let's call this angle "C". Then:
   
   
   Formula:

   C = 90 - A 

   If the new spot is due north of the target, then the bearing is 360 degrees or 0 degrees.

Let me know if you have any questions or if there's anything else I can assist you with.

On Dec 13, 4:36*am, Donald Ross wrote:
Good Morning,

I would like to better understand the method or methods used to calculate and determine bearing and distance from a known point based on observation(s) from two known points.

Let me explain mo Lets use a 60,60,60 triangle so there is no confustion about what side is the base. I have two observation towers, Tower Left, and Tower Right. and the tip or top is the target. *If I observe a bomb/explosion/ect... at a point that is 10 degrees left of the target from the left tower and 10 degrees right of the target from the right tower. I now have a new triangle that is 70,70,40 and I can calculate the leg lengths. where I am lost is trying to determine the bearing & distance from the target to the new spot. *using this example it would be due north of the target i.e. 360 or 12 o'clock, but I am not sure how to find distance at this point. *any assistance in a medthod or solution would be greatly appreciated. *Don

One way is to find the coordinates of the target and the bomb
separately then find the distance and bearing of the bomb from the
target.

Assume that the base of your triangle is your x axis, the left hand
tower is on 0 and the right hand tower is on D.

The target makes a triangle with base angles A in the left and B on
the right. The top angle is C = 180 - A - B. The left side is L.

The sine rule says L/sinB = D/sinC. You know B, D and C so this gives
L. This is what you call the leg length. The coordinates of the
target are x1 = LcosA and y1 = LsinA. In your simplified case, A and
B are 60 but the above works for any angles.

Repeat the calculations only using the appropriate angles for the
bomb. This gives you another set of x2 and y2 as the coordinates of
the target. We now have the ends of the target/bomb line and can draw
a right angles triangle.

The distance from target to bomb = SQRT((y2-y1)^2+(x2-x1)^2).
Pythagoras
The angle from the x direction is ATAN((y2-y1)/(x2-x1)) or from
straight ahead, ATAN((x2-x1)/(y2-y1))

Snags:
1 Excel works in radians, not degrees so you will need to convert
things at the beginning and the end. C = 180 - A - B becomes C = PI()
- A - B.
2 ATAN only give angles from -pi/2 to pi/2 or from -90 to 90.
Sometimes you will
need to add 180

Cheers

xt