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.
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,
Learning the notations in triangulation:
Learning the triangulation formulas:
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` = 30^{o} and `beta` = 60^{o} and l = 8.
Solution:
The distance formula is d = `(l.sinalpha.sinbeta)/(sin(alpha+beta))`
Given values are `alpha` = 30^{o} and `beta` = 60^{o} 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` = 45^{o} and `beta` = 75^{o} , l = 5.
Solution: The distance is d = 3.93.