# Interactive Graphical Triangle

x-min= x-max=
y-min= y-max=
P1 =
P2 =
P3 =

#### Interactive graphical

Circle Ellipse Trapeze Parallelogram

#### Trigonometry

Trigonometry Angle, opposite cathetus Angle, adjacent cathetus Cathetus Cathetus, hypotenuse 2 sides, 1 angle 2 angles, 1 side 3 sides Tower height Cross bearing Triangle of forces Hansens task

#### Trigonometric functions

Tables Sine, Cosine, Tangent Power and n-th argument Triangle

## Triangle with the edge points P1, P2 and P3

Move the points in the grafic or define the point coordinates in the numeric field.

### Angle sum

The angle sum in triangle is 180°.

$\alpha +\beta +\gamma =180°$

### Median

By a median is meant a straight line connecting a vertex of the triangle to the center of the opposite side. The sides of a triangle intersect at the center of gravity of the triangle. The length of the median of side a is:

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

### Bisecting

A bisector is a straight line which divides an angle of the triangle into two equal parts. The bisectors of a triangle intersect at the center of the circle. The length of the bisector of the angle α is:

${l}_{\alpha }=\frac{\sqrt{bc{\left(b+c\right)}^{2}-{a}^{2}}}{b+c}$

### Height hc on side c

The height is defined as a straight line (at 90°) on one side and connecting the side to the opposite corner. The length of the height on the side c is:

${h}_{c}=a\cdot \mathrm{sin}\left(\beta \right)=b\cdot \mathrm{sin}\left(\alpha \right)$

### Perpendicular

A perpendicular of a side is a line that divides one side of the triangle into two equal parts and is perpendicular to the side. The median of a triangle intersect at the center of the circumcircle.

The perimeter is a circle passing through the vertices of the triangle.

$r=\frac{s}{4\cdot \mathrm{cos}\left(\frac{\alpha }{2}\right)\cdot \mathrm{cos}\left(\frac{\beta }{2}\right)\cdot \mathrm{cos}\left(\frac{\gamma }{2}\right)}$

with

$s=\frac{1}{2}\left(a+b+c\right)$

The incircle is a circle that touches each side of the triangle.

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

### Area A

$A=\frac{1}{2}a\cdot b\cdot \mathrm{sin}\left(\gamma \right)$

### Circumference U

$U=a+b+c$

### Heronische area formula

$A=\rho s=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

### Cemter line

The center line connects the centers of two triangular sides. It is parallel to the third side and half as long.

### Rectangular triangle

The cathetes a and b form a right angle. In oposite to the right angle is the hypotenuse c. The theorem of Pythagoras holds:

${c}^{2}={a}^{2}+{b}^{2}$

### Area A in the rectangular triangle

$A=\frac{a\cdot b}{2}$