Scalene Triangle

on . Posted in Plane Geometry

  • scalene triangle 3Scalene triangle (a two-dimensional figure) is 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 is a circle that passes through all the vertices of a two-dimensional figure.
  • Inscribed circle is the Iargest circle possible that can fit on the inside of a two-dimensional figure.
  • Semiperimeter is one half of the perimeter.
  • x + y + z = 180°
  • 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
  • 3 edges
  • 3 vertexs

Scalene Triangle Index

scalene triangle 5hscalene triangle 5mscalene triangle 5t

scalene triangle 4

 

 

 

 

 

 

 

Angle bisector of a Scalene Triangle formulas

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

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

Symbol English Metric
\(\large{ t_a }\) = angle bisector \(\large{ in}\) \(\large{ mm }\)
\(\large{ \theta }\) = angle \(\large{deg}\) \(\large{rad}\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Area of a Scalene Triangle formulas

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

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

Symbol English Metric
\(\large{ A_{area} }\) = area \(\large{ in^2}\) \(\large{ mm^2}\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Circumcircle of a Scalene Triangle formulas

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

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

Symbol English Metric
\(\large{ R }\) = outcircle \(\large{ in}\) \(\large{ mm }\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)
\(\large{ s }\) = semiperimeter \(\large{ in}\) \(\large{ mm }\)

 

Height of a Scalene Triangle formulas

\(\large{ h_a = c \; sin\; B  }\) 

\(\large{ h_a = b \; sin\; C  }\)

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

Symbol English Metric
\(\large{ h_a }\) = height \(\large{ in}\) \(\large{ mm}\)
\(\large{ B, C }\) = angle \(\large{ deg}\) \(\large{ rad}\)
\(\large{ A_{area} }\) = area \(\large{ in^2}\) \(\large{ mm^2 }\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Inscribed Circle of a Scalene Triangle formula

\(\large{ r =   \sqrt  {   \frac  {  \left( s \;-\; a  \right)  \; \left( s \;-\; b  \right) \;  \left( s \;-\; c  \right)  }  { s }   }  }\) 
Symbol English Metric
\(\large{ r }\) = incircle \(\large{ in}\) \(\large{ mm }\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Median of a Scalene Triangle formula

\(\large{ m_a =  \sqrt { \frac { 2\;b^2 \;+\; 2\;c^2  \;-\; a^2 }  {2}   } }\) 
Symbol English Metric
\(\large{ m_a }\) = median \(\large{ in}\) \(\large{ mm }\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Perimeter of a Scalene Triangle formula

\(\large{ P = a + b + c }\) 
Symbol English Metric
\(\large{ P }\) = perimeter \(\large{ in}\) \(\large{ mm }\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Semiperimeter of a Scalene Triangle formula

\(\large{ s =   \frac{ a \;+\; b \;+\; c }{ 2  }   }\) 
Symbol English Metric
\(\large{ s }\) = semiperimeter \(\large{ in}\) \(\large{ mm }\)
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Side of a Scalene Triangle formulas

\(\large{ a = P - b - c   }\)

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

\(\large{ b = P - a - c   }\) 

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

\(\large{ c = P - a - b   }\)

Symbol English Metric
\(\large{ a, b, c }\) = edge \(\large{ in}\) \(\large{ mm }\)
\(\large{ A_{area} }\) = area \(\large{ in^2}\) \(\large{ mm^2 }\)
\(\large{ P }\) = perimeter \(\large{ in}\) \(\large{ mm }\)

 

Trig Functions

Find A
  • given a c :  \(\; sin \; A= a \div c \)
  • given b c :  \(\; cos \; A= b \div c \)
  • given a b :  \(\; tan \; A= a \div b \)
Find B
  • given a c :  \(\; sin \; B= a \div c \)
  • given b c :  \(\; cos \; B= b \div c \)
  • given a b :  \(\; tan \; B= b \div a \)
 Find a
  • given A c :  \(\; a= c*sin \; A \)
  • given A b :  \(\; a= b*tan \; A \)
Find b
  • given A c :  \(\; b= c*cos \; A \)
  • given A a :  \(\; b= a \div tan \; A \)
Find c
  • given A a :  \(\; c= a \div sin \; A \)
  • given A b :  \(\; c= b \div cos \; A \)
  • given a b :  \(\; c= \sqrt { a^2+b^2 } \)
Find Area
  • given a b :  \(\; Area= a\;b \div 2 \)

 

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Tags: Triangle