# Scalene Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

## Scalene Triangle

• An scalene triangle is when no sides or angles are equal.
• 3 edges
• 3 vertexs
• $$x\;+\;y\;+\;z\;=\;180°$$.
• Sidess:  $$a$$,  $$b$$,  $$c$$
• Angles:  $$A$$,  $$B$$,  $$C$$
• Area:  $$K$$
• Perimeter:  $$P$$
• Semi-perimeter:  $$s$$  -  One half of the perimeter
• Inradius of triangle:  $$r$$
• Outradius (circumcircle) of triangle:  $$R$$
• Height:  $$h_a$$,  $$h_b$$,  $$h_c$$
• Median:  $$m_a$$,  $$m_b$$,  $$m_c$$  -  A line segment from a vertex (coiner 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

An angle bisector is a line that splits an angle into two equal angles.

### Angle bisector of a Scalene Triangle formula

$$t_a = 2bc \; cos \; \frac { \frac {A}{2} } { b+c }$$

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

Where:

$$t_a$$ = angle bisector

$$a$$ = side

$$A$$ = angle

## Area of a Scalene Triangle

### Area of a Scalene Triangle formula

$$K = \frac {hb} {2}$$

$$K = ab \frac {\sin y} {2}$$

Where:

$$K$$ = area

$$b$$ = side

## Circumcircle of a Scalene Triangle

The radius of a circumcircle (outer) of a triangle if given all three sides $$( R )$$.

### Circumcircle of a Scalene Triangle formula

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

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

Where:

$$R$$ = outcircle

$$a, b, c$$ = side

$$s$$ = semiperimeter

## Height of a Scalene Triangle

### Height of a Scalene Triangle formula

$$h_a = c \; sin \; B$$

$$h_a = b \; sin \; C$$

$$h_a = 2 \frac {K}{a}$$

Where:

$$h_a$$ = height

$$a, b, c$$ = side

$$B, C$$ = angle

$$K$$ = area

## Inscribed Circle of a Scalene Triangle

The radius of a inscribed circle (inner) of a triangle if given all three sides $$( r )$$.

### Inscribed Circle of a Scalene Triangle formula

$$r = \sqrt { \frac { \left( s - a \right) \left( s - b \right) \left( s - c \right) } { s } }$$

Where:

$$r$$ = incircle

$$a, b, c$$ = side

## Median of a Scalene Triangle

Median is a line segment from a vertex (coiner point) to the midpoint of the opposite side.

### Median of a Scalene Triangle formula

$$m_a = \sqrt { \frac { 2b^2 + 2c^2 - a^2 } {2} }$$

Where:

$$m_a$$ = median

$$a, b, c$$ = side

## Perimeter of a Scalene Triangle

### Perimeter of a Scalene Triangle formula

$$P = a + b + c$$

Where:

$$P$$ = perimeter

$$a, b, c$$ = side

## Semiperimeter of a Scalene Triangle

### Semiperimeter of a Scalene Triangle formula

$$s = \frac { a + b + c } { 2 }$$

Where:

$$s$$ = semiperimeter

$$a, b, c$$ = side

## Side of a Scalene Triangle

### Side of a Scalene Triangle formula

$$a = P - b - c$$

$$a = 2 \frac {K} {b\;\sin y}$$

$$b = P - a - c$$

$$b = 2 \frac {K}{h}$$

$$c = P - a - b$$

Where:

$$a, b, c$$ = side

$$P$$ = perimeter

$$K$$ = area