Right Triangle Calculator

Name: Right Triangle - Geometry Calculator
Author: Jürgen Kummer

Calculations at a right triangle. A right triangle has one right angle of 90 degrees and two acute angles of less than 90 degrees.
Enter at a, b and c two values and choose the number of decimal places. Then click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units.

Formulas:

a^{2} + b^{2} = c^{2} (Pythagorean theorem)

p = \frac{a^{2}}{c}

q = \frac{b^{2}}{c}

h = \sqrt{p \cdot q}

Perimeter = a + b + c

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

α = \arccos (\frac{b^{2} + c^{2} - a^{2}}{2 b c})

β = \arccos (\frac{a^{2} + c^{2} - b^{2}}{2 a c})

γ = \frac{π}{2} = 90 °

r_{c} = \frac{c}{2}

r_{i} = \frac{a + b - c}{2}

m_{a} = \frac{\sqrt{2 \cdot (b^{2} + c^{2}) - a^{2}}}{2}

m_{b} = \frac{\sqrt{2 \cdot (c^{2} + a^{2}) - b^{2}}}{2}

m_{c} = \frac{\sqrt{2 \cdot (a^{2} + b^{2}) - c^{2}}}{2}

Catheti (legs), hypotenuse, median lines, heights, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The heights of the legs are identical with each other leg. The centroid of the right triangle is at the intersection of the median lines. The intersection of the bisecting lines is the center of the incircle. The center of the circumcircle is the intersection of the perpendicular bisectors of the legs and the center of the hypotenuse.

perimeter p, area A

legs and hypotenuse

heights

hypotenuse segments p and q

median lines and centroid

bisecting lines and incircle

perpendicular bisectors and circumcircle

A right triangle is created when you cut a rectangle in half diagonally. The right triangle forms the basis for the Pythagorean theorem and for trigonometric functions such as sine and cosine. The longest side, the one opposite the right angle, is called the hypotenuse, the other two are called catheti or legs. Regarding one of the acute angles, there is the adjacent angle, which lies against the angle, and the opposite angle, which lies opposite this angle. The Pythagorean theorem states that the square of the hypotenuse is equal to the squares of the legs combined. Since the hypotenuse is also the diagonal of the corresponding rectangle, you can use this to calculate the length of diagonals opposite to a right angle as the root of the sum of the squares of the two sides. The Pythagorean theorem is a fundamental theorem of Euclidean geometry and is of outstanding importance; Pythagoras of Samos is said to have been the first to prove it.

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