High School Honors Institute
Department of Applied Mathematics
Triangulation and Trilateration
Triangulation and trilateration are methods one can use to
determine location assuming a few things are known.
Triangulation
(Triangle not drawn to scale.) Joanna is standing at point B.
If the three closest satellites are located at:
| Satellite | | Location
|
| Q1 | = | (0,2,1)
|
| Q2 | = | (2,-1,1)
|
| Q3 | = | (0,0,2)
|
and the angles are:
| Angle | | Value
|
| a1 | = | 50.77 o
|
| b1 | = | 11.30 o
|
| a2 | = | 7.13 o
|
| b2 | = | 43.09 o
|
| a3 | = | 61.87 o
|
| b3 | = | 39.23 o
|
- What are the coordinates of where Joanna is standing?
- What can we say about Joanna's location if one of the angles is off by 1o?
Trilateration
(Triangle not drawn to scale.) Joe is standing at point A. If
the three closest satellites are located at:
| Satellite | | Location
| | P1 | = | (0,2,1)
|
| P2 | = | (1,5,2)
|
| P3 | = | (6,7,3)
|
and if
| Side | | Length
| | l1 | = | 2.236
|
| l2 | = | 3.162
|
| l3 | = | 7.071
|
- What are the coordinates of where Joe is standing?
- If we
mistakenly assumed that l3=7.000 instead of 7.071, how far
off from Joe's location would we be?
Some Useful Formulas
