 Interactive Graphical Triangle

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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

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