Scalene Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • scalene triangle 3A two-dimensional figure where all three sides are different lengths and all three angles are different angles.
  • Angle bisector of a scalene triangle is a line that splits an angle into two equal angles.
  • Median of a scalene triangle is a line segment from a vertex (coiner point) to the midpoint of the opposite side.
  • Circumcircle (R) is a circle that passes through all the vertices of a two-dimensional figure.
  • Inscribed circle (r) is the Iargest circle possible that can fit on the inside of a two-dimensional figure.
  • Semiperimeter (s) is one half of the perimeter.
  • 3 edges
  • 3 vertexs
  • \(x\;+\;y\;+\;z\;=\;180°\).
  • Sides:  \(a\),  \(b\),  \(c\)
  • Angles:  \(A\),  \(B\),  \(C\)
  • Height:  \(h_a\),  \(h_b\),  \(h_c\)
  • Median:  \(m_a\),  \(m_b\),  \(m_c\)  -  A line segment from a vertex (corner 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

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Angle bisector of a Scalene Triangle formula

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

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

Where:

\(\large{ t_a }\) = angle bisector

\(\large{ A }\) = angle

\(\large{ a, b, c }\) = edge

Area of a Scalene Triangle formula

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

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

Where:

\(\large{ K }\) = area

\(\large{ a, b, c }\) = edge

Circumcircle of a Scalene Triangle formula

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

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

Where:

\(\large{ R }\) = outcircle

\(\large{ a, b, c }\) = edge

\(\large{ s }\) = semiperimeter

Height of a Scalene Triangle formula

\(\large{ h_a = c \; sin\; B  }\)

\(\large{ h_a = b \; sin\; C  }\)

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

Where:

\(\large{ h_a }\) = height

\(\large{ a, b, c }\) = edge

\(\large{ B, C }\) = angle

\(\large{ K }\) = area

Inscribed Circle of a Scalene Triangle formula

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

Where:

\(\large{ r }\) = incircle

\(\large{ a, b, c }\) = edge

Median of a Scalene Triangle formula

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

Where:

\(\large{ m_a }\) = median

\(\large{ a, b, c }\) = edge

Perimeter of a Scalene Triangle formula

\(\large{ P = a + b + c }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ a, b, c }\) = edge

Semiperimeter of a Scalene Triangle formula

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

Where:

\(\large{ s }\) = semiperimeter

\(\large{ a, b, c }\) = edge

Side of a Scalene Triangle formula

\(\large{ a = P - b - c   }\)

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

\(\large{ b = P - a - c   }\)

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

\(\large{ c = P - a - b   }\)

Where:

\(\large{ a, b, c }\) = edge

\(\large{ P }\) = perimeter

\(\large{ K }\) = area

 

Tags: Equations for Triangle