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Scalene Triangle

  • 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

 

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scalene triangle 4

 

 

 

 

 

Angle bisector of a Scalene Triangle formulas

\( t_a \;=\;   2\cdot b \cdot c \cdot cos \left( \dfrac{ \dfrac{A}{2} }{ b + c } \right) \) 

\( t_a \;=\;   \sqrt { b\cdot c \cdot \dfrac{ 1 -  a^2 }{  \left( b + c \right)^2  }   } \) 
Symbol English Metric
\( t_a \) = angle bisector \( in\) \( mm \)
\( \theta \) = angle \(deg\) \(rad\)
\( a, b, c \) = edge \( in\) \( mm \)

 

Area of a Scalene Triangle formulas

\( A_{area} \;=\;   \dfrac{ h \cdot b}{2} \) 

\( A_{area} \;=\;   a \cdot b \cdot \dfrac{ sin( y)  }{2} \) 
Symbol English Metric
\( A_{area} \) = area \( in^2\) \( mm^2 \)
\( a, b, c \) = edge \( in\) \( mm \)

 

Circumcircle of a Scalene Triangle formulas

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

\( R \;=\;    \dfrac{ a \cdot b \cdot c   }{  4 \cdot  \sqrt{  s\cdot  \left( s - a  \right)  \cdot   \left( s - b  \right)  \cdot   \left( s - c  \right)  }     }  \)
Symbol English Metric
\( R \) = outcircle \( in\) \( mm \)
\( a, b, c \) = edge \( in\) \( mm \)
\( s \) = semiperimeter \( in\) \( mm \)

 

Height of a Scalene Triangle formulas

\( h_a \;=\;   c \cdot sin( B)  \) 

\( h_a \;=\;   b \cdot sin( C)  \)

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

 

Inscribed Circle of a Scalene Triangle formula
\( r \;=\;     \sqrt{   \dfrac{  \left( s - a  \right)  \cdot \left( s - b  \right) \cdot  \left( s - c  \right)  }{ s }   }  \) 
Symbol English Metric
\( r \) = incircle \( in\) \( mm \)
\( a, b, c \) = edge \( in\) \( mm \)

 

Median of a Scalene Triangle formula
\( m_a \;=\;   \sqrt{ \dfrac{ 2 \cdot b^2 + 2 \cdot c^2  - a^2 }{ 2}   } \) 
Symbol English Metric
\( m_a \) = median \( in\) \( mm \)
\( a, b, c \) = edge \( in\) \( mm \)

 

Perimeter of a Scalene Triangle formula
\( P \;=\;   a + b + c \) 
Symbol English Metric
\( P \) = perimeter \( in\) \( mm \)
\( a, b, c \) = edge \( in\) \( mm \)

 

Semiperimeter of a Scalene Triangle formula
\( s \;=\;     \dfrac{ a + b + c }{ 2  }   \) 
Symbol English Metric
\( s \) = semiperimeter \( in\) \( mm \)
\( a, b, c \) = edge \( in\) \( mm \)

 

Side of a Scalene Triangle formulas

\( a \;=\;   P - b - c   \)

\( a \;=\;   2 \cdot \dfrac{A_{area}  }{ b \cdot sin( y)  } \) 

\( b \;=\;   P - a - c   \) 

\( b \;=\;   2 \cdot \dfrac{A_{area} }{  h } \)

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

 

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

 

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