# Online Interactive Triangle

## Interactive Triangle calculator

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

Scale:
Number of digits =
Side length:
a=
b=
c=
Heigths:
ha=
hb=
hc=
Angles in degree:
α=
β=
γ=
α=
β=
γ=
Median lines:
ma=
mb=
mc=
Bisector lines:
lα=
lβ=
lγ=
Circum­ference U=
Area =
R=
r=

Point coordinates x, y

P1 =
P2 =
P3 =

Axes ranges

x-min=
x-max=
y-min=
y-max=
Sides:
P1, P2, P3:
Incircle:
Circumcircle:
Heights:
Median lines:
Perpendicular lines:
Bisector lines:

## Triangle calculation formulas

### Angular 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:

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

The length of the median of side b is:

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

The length of the median of side c is:

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

### 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 incircle.

The length of the bisector of the angle α is:

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

The length of the bisector of the angle β is:

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

The length of the bisector of the angle γ is:

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

### Height

The height is defined as a straight line at 90° on one side and connecting the side to the opposite corner. The diagram shows the three heights in black dotted lines.

The length of the height on the side a is:

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

The length of the height on the side b is:

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

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 bisector

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 perpendicular bisector lines of a triangle intersect at the center of the circumcircle.

The circumcircle 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.

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

### Triangle area A

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

### Triangle circumference U

$U=a+b+c$

### Heronische area formula

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

### Center line

The center line connects the centers of two triangle 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

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

Essential for the calculations in general triangle are the cosine and the sine law and the relationship of the trigonometric functions.

### Sine law

$\frac{a}{\mathrm{sin}\left(\alpha \right)}=\frac{b}{\mathrm{sin}\left(\beta \right)}=\frac{c}{\mathrm{sin}\left(\gamma \right)}$

### Cosine law

${a}^{2}={b}^{2}+{c}^{2}-2bc\mathrm{cos}\left(\alpha \right)$

${b}^{2}={a}^{2}+{c}^{2}-2ac\mathrm{cos}\left(\beta \right)$

${c}^{2}={a}^{2}+{b}^{2}-2ab\mathrm{cos}\left(\gamma \right)$

### Screenshot of the Image

Print or save the image via right mouse click.

## Releated sites

Here is a list of of further useful sites:

Index Trigonometric calculations Circle Ellipse Parallelogram Rectangle