Right triangle
Calculation of a right triangle from a given side and angle
This function calculates the most important parameters of a right triangle from a side length and the angle α. As a result, the cathetus, hypotenuse, height, circumference, area, hypotenuse sections and the angles are displayed.
To perform the calculation, select the side length you know and enter its values and the angle. Then click on the 'Calculate' button.
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Formulas and description for right triangles
In a right angle, the cathets are the two sides that lie against the right angle. The hypotenuse is the side opposite the right angle. The height is measured from the right angle to the hypotenuse. The hypotenuse sections are the sections of the hypotenuse from the respective corner to the point where the line of height meets the hypotenuse.
Hypotenuse c
\(\displaystyle c=\sqrt{a^2+b^2} \) \(\displaystyle c= \frac{a}{sin(α)}\) \(\displaystyle c= \frac{b}{cos(α)}\)
Cathete a
\(\displaystyle a=\sqrt{c^2-b^2}\) \(\displaystyle a=b·tan(α)\) \(\displaystyle a=c·sin(α)\)
Cathete b
\(\displaystyle a=\sqrt{c^2-a^2} \) \(\displaystyle b=\frac{a}{tan(α)}\) \(\displaystyle b=c·cos(α)\)
Area A
\(\displaystyle A = \frac{ a · b}{2} \) \(\displaystyle A = \frac{ c · h}{2} \)
Perimeter P
\(\displaystyle P=a+b+c \)
Height h
\(\displaystyle h = \frac{ a · b}{c} \) \(\displaystyle h=\sqrt{ p · q} \)
Segment p
\(\displaystyle p= \frac{a^2}{c} \)
Segment q
\(\displaystyle q = \frac{b^2}{c} \)
Angle α
\(\displaystyle α = arcsin \left( \frac{a}{c} \right) \) \(\displaystyle α = arccos \left( \frac{b}{c} \right) \)
Angle β
\(\displaystyle β = arcsin \left( \frac{b}{c} \right) \) \(\displaystyle β = arccos \left( \frac{a}{c} \right) \)
Bisector of a triangle
Equilateral triangle
Right triangles
Right triangle, given 1 side and 1 angle
Isosceles right triangles
Isosceles triangles
Triangle area, given 2 sides and 1 anglee
Triangle area, given 1 side and 2 angles
Triangle, Incircle, given 3 sides
Area of a triangle given base and height
Triangle vertices, 3 x/y points
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