Scalene Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Scalene Trianglescalene triangle 4scalene triangle 3

  • An scalene triangle is when no sides or angles are equal.
  • 3 edges
  • 3 vertexs
  • \(x\;+\;y\;+\;z\;=\;180°\).
  • Sidess:  \(a\),  \(b\),  \(c\)
  • Angles:  \(A\),  \(B\),  \(C\)
  • Area:  \(K\)
  • Perimeter:  \(P\)
  • Semi-perimeter:  \(s\)  -  One half of the perimeter
  • Inradius of triangle:  \(r\)
  • Outradius (circumcircle) of triangle:  \(R\)scalene triangle 5hscalene triangle 5mscalene triangle 5t
  • Height:  \(h_a\),  \(h_b\),  \(h_c\)
  • Median:  \(m_a\),  \(m_b\),  \(m_c\)  -  A line segment from a vertex (coiner point) to the midpoint of the opposite side
  • Angle bisectors:  \(t_a\),  \(t_b\),  \(t_c\)  -  A line that splits an angle into two equal angles

 

 

 

Angle bisector of a Scalene Triangle

An angle bisector is a line that splits an angle into two equal angles.

Angle bisector of a Scalene Triangle formula

\(t_a = 2bc \; cos \;  \frac { \frac {A}{2} }  { b+c }  \)

\(t_a = \sqrt { bc  \frac { 1-a^2 }{   \left( b+c \right)^2  }   } \)

Where:

\(t_a\) = angle bisector

\(a\) = side

\(A\) = angle

Area of a Scalene Triangle

Area of a Scalene Triangle formula

\(K = \frac {hb} {2} \)

\(K = ab \frac {\sin y} {2} \)

Where:

\(K\) = area

\(b\) = side

Circumcircle of a Scalene Triangle

The radius of a circumcircle (outer) of a triangle if given all three sides \(( R )\).

Circumcircle of a Scalene Triangle formula

\(R =  \sqrt {   \frac  { a^2  b^2  c^2 }  {  \left( a + b + c  \right)      \left( - a + b + c  \right)      \left( a - b + c  \right)        \left( a + b - c  \right)    }     }  \)

\(R =  \frac  { a  b  c }   {   4   \sqrt  {  s  \left( s - a  \right)      \left( s - b  \right)        \left( s - c  \right)  }     }  \)

Where:

\(R\) = outcircle

\(a, b, c\) = side

\(s\) = semiperimeter

Height of a Scalene Triangle

Height of a Scalene Triangle formula

\(h_a = c \; sin \; B  \)

\(h_a = b \; sin \; C  \)

\(h_a = 2 \frac {K}{a} \)

Where:

\(h_a\) = height

\(a, b, c\) = side

\(B, C\) = angle

\(K\) = area

Inscribed Circle of a Scalene Triangle

The radius of a inscribed circle (inner) of a triangle if given all three sides \(( r )\).

Inscribed Circle of a Scalene Triangle formula

\(r =   \sqrt  {   \frac  {  \left( s - a  \right)   \left( s - b  \right)   \left( s - c  \right)  }  { s }   }  \)

Where:

\(r\) = incircle

\(a, b, c\) = side

Median of a Scalene Triangle

Median is a line segment from a vertex (coiner point) to the midpoint of the opposite side.

Median of a Scalene Triangle formula

\(m_a =  \sqrt { \frac { 2b^2 + 2c^2  - a^2 }  {2}   } \)

Where:

\(m_a\) = median

\(a, b, c\) = side

Perimeter of a Scalene Triangle

Perimeter of a Scalene Triangle formula

\(P = a + b + c \)

Where:

\(P\) = perimeter

\(a, b, c\) = side

Semiperimeter of a Scalene Triangle

Semiperimeter of a Scalene Triangle formula

\(s =   \frac  { a + b + c }  { 2  }   \)

Where:

\(s\) = semiperimeter

\(a, b, c\) = side

Side of a Scalene Triangle

Side of a Scalene Triangle formula

\(a = P - b - c   \)

\(a = 2 \frac {K} {b\;\sin y} \)

\(b = P - a - c   \)

\(b = 2 \frac {K}{h} \)

\(c = P - a - b   \)

Where:

\(a, b, c\) = side

\(P\) = perimeter

\(K\) = area

 

Tags: Equations for Triangle