Scalene Triangle

Scalene 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

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 : \(\; Area \;=\; \dfrac{ a \cdot b }{ 2 }\)