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 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
\(\large{ A_{area} = \frac {h\;b} {2} }\)
\(\large{ A_{area} = a\;b\; \frac {\sin y} {2} }\)
Where:
\(\large{ A_{area} }\) = 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
\(\large{ h_a = c \; sin\; B }\)
\(\large{ h_a = b \; sin\; C }\)
\(\large{ h_a = 2\; \frac {A_{area}}{a} }\)
Where:
\(\large{ h_a }\) = height
\(\large{ a, b, c }\) = edge
\(\large{ B, C }\) = angle
\(\large{ A_{area} }\) = 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
\(\large{ a = P - b - c }\)
\(\large{ a = 2\; \frac {A_{area}} {b\;\sin y} }\)
\(\large{ b = P - a - c }\)
\(\large{ b = 2\; \frac {A_{area}}{h} }\)
\(\large{ c = P - a - b }\)
Where:
\(\large{ a, b, c }\) = edge
\(\large{ P }\) = perimeter
\(\large{ A_{area} }\) = area
Tags: Equations for Triangle