Distance of a Triangle

              

                                                     

A,B and C are three non-collinear points. The figure which surronded by segments of the lines AB, BC and CA is called  triangle having A,B and C as its vertices. All the points situated on AB, BC and CA are included in this triangle. In a triangle, an exterior angle is greater than either of the interior opposite anglesThe sum of all the angles in any triangle is 180º.

 There are types of triangle

• Equilateral triangles,
• Isosceles triangles 
• Scalene triangles
• Right Triangles

Understanding The Formula for Distance is always challenging for me but thanks to all math help websites to help me out.

Types of Triangles:

Right Triangles:

         In a right triangle is a triangle with a 90° right angle triangle

                                    

 

Equilateral Triangles

In equilateral triangle  all three sides are in equal length also  three angles are  equal and they are  60º in each.

                                    

Isosceles Triangles

In isosceles triangle, two sides are in equal  length. The angles opposite are also equal sides

                                    

Scalene Triangles

 A scalene triangle has no equl sides of its length. Its angles are also all different in measure.

                                   

Finding distance Of a Triangle:

Example 1:

Find the distance of triangle whose points  are (-2, -3), (-4, 4), (5,8)

Solution:

to find distance of triangle where  (x₁,y1)=(-2,-3)

(_x2,y₂)=(-4,4)

                                                         

sqrt((x2-x1)^2 +(y2-y1)^2)`

   
=`sqrt(((-4-(-2))^2+4-(-3)^2))`
=`sqrt((-4+2)^2+(4+3)^2)`
=`sqrt((-2)^2+7^2)`
=`sqrt(4+49)`
length of one side  =7.28
similarly we can find another sides

Example 2:

Find the distance of triangle whose points  are (2, 3), (4, 6),(5,0)

Solution:

to find distance of triangle where  (x₁,y1)=(2,3)

(_x2,y₂)=(4,6)

sqrt((x2-x1)^2 +(y2-y1)^2)`

=`sqrt((4-2)^2+(6-3)^2))`
=`sqrt((2)^2+3^2)`
=`sqrt(4+
length of one side =`sqrt(13)`
similarly we can find another side lengths

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Example 3:

            Find the distance of triangle whose points  are (1, -3), (2, 5),(4,6)

Solution:

          to find distance of triangle where  (x₁,y1)=(1,-3)

                                                               (_x2,y₂)=(2,5)

                                                         

                    `sqrt((x2-x1)^2 +(y2-y1)^2)`

   
                   =`sqrt((2-1)^2+(5-(-4))^2))`
             
                   =`sqrt((1)^2+9^2)`
                   =`sqrt(1+81)`
                   =`sqrt(82)`

               Length of one side =9.05
Similarly we can find another two side lengths.