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=
Angles in radian:
α=
β=
γ=
Median lines:
ma=
mb=
mc=
Bisector lines:
lα=
lβ=
lγ=
Circum­ference U=
Area =
Circle radii
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°.

α+β+γ=180°

Median

triangle-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:

ma=2b2+c2-a22

The length of the median of side b is:

mb=2a2+c2-b22

The length of the median of side c is:

mc=2a2+b2-c22

Bisecting

triangle-bisection

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:

lα=bcb+c2-a2b+c

The length of the bisector of the angle β is:

lβ=aca+c2-b2a+c

The length of the bisector of the angle γ is:

lγ=bab+a2-c2b+a

Height

triangle-heights

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:

ha=bsinγ=csinβ

The length of the height on the side b is:

hb=asinγ=csinα

The length of the height on the side c is:

hc=asinβ=bsinα

Perpendicular bisector

triangle-perpendicular-lines

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.

Circumcircle radius r

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

r=s4cosα2cosβ2cosγ2

with

s=12a+b+c

Incircle radius ρ

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

ρ=s-as-bs-cs

Triangle area A

A=12absinγ

Triangle circumference U

U=a+b+c

Heronische area formula

A=ρs=ss-as-bs-c

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:

c2=a2+b2

Area A in the rectangular triangle

A=ab2

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

Sine law

asinα=bsinβ=csinγ

Cosine law

a2=b2+c2-2bccosα

b2=a2+c2-2accosβ

c2=a2+b2-2abcosγ

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Releated sites

Here is a list of of further useful sites:

Index Trigonometric calculations Circle Ellipse Parallelogram Rectangle