# Scalene Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• A 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

### 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