# Learning Triangulation

Introduction :

The students are learning the math a topic using online articles and tutorials.The collection of triangles is called as triangulation and it is the process of location of point determination by measuring angles. We are learning the trigonometry by using the triangulation. The triangulation is used to measure the three-dimension systems. Now we are going to see about learning triangulation.

## Explanation for learning triangulation

Learning the triangulation in online:

The triangulation is set of triangles and the adjacent triangles are sharing the each triangle side. Some requirements are used for triangulation satisfaction. They are,

• The triangle’s interiors are pair wise disjoint.
• The one side of each triangle is common edge of two triangles.
• The homeomorphic to a square is property of union of triangles.

Learning the notations in triangulation:

• Triangulation is T.
• The number of triangles is represented by N.
• The union of triangle is D.
• The number of boundary vertices is` V_(B)` .
• The number of interior vertices is` V_(I)` .

Learning the triangulation formulas:

• The total number of vertices V =` V_(B) + V_(I)` .
• Total number of triangles N = `V_(B) + 2V_(I) -2` .
• The distance of unknown point is d = `(l.sinalpha.sinbeta)/(sin(alpha+beta))` .

Example problems for learning triangulation:

Problem 1: Find out the number of vertices and number of triangles in given triangulation.

Solution:

The number of vertices in boundary is `V_(B)` = 3.

The number of vertices in interior is `V_(I)` = 1.

The total number of vertices is V = ` V_(B) + V_(I)`

V = 3 + 1 = 4.

The number of triangles is N = `V_(B)` + 2`V_(I)` - 2 = 3 + 2(1) - 2 = 3 + 2 - 2 = 3.

Therefore, the total number of vertices is 4 and total number of triangles is 3.

Problem 2: Find out the distance of unknown side with given two angle values.

`alpha` = 30o and `beta` = 60o and l = 8.

Solution:

The distance formula is d = `(l.sinalpha.sinbeta)/(sin(alpha+beta))`

Given values are `alpha` = 30o and `beta` = 60o and l = 8.

d = `(8.sin30.sin60)/(sin(30+60))`

d = 3.46.

Exercise problems for learning triangulation:

1. Find out the total number of triangle with `V_(B)` = 5 and `V_(I)` = 3.

Solution: The total number of triangles is N = 9.

2. Find out the distance of unknown points from `alpha` = 45o and `beta` = 75o , l = 5.

Solution: The distance is d = 3.93.