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xGeometry

Right Triangle

Minimum Cathetus
$$c_{1}$$
Maximum Cathetus
$$c_{2}$$
Hypotenuse
$$i$$
Height
$$h$$
Min Projection
$$p_{1}$$
Max Projection
$$p_{2}$$
$$2p = i + c_{1} + c_{2}$$
Perimeter
$$A = \frac{c_{1} \times c_{2}}{2}$$
Area
$$c_{1} = \frac{A \times 2}{c_{2}}$$
$$c_{2} = \frac{A \times 2}{c_{1}}$$
$$A = \frac{i \times h}{2}$$
Area
$$i = \frac{A \times 2}{h}$$
$$h = \frac{A \times 2}{i}$$
Pythagoras' theorem
$$i = \sqrt{ {c_{1}}^2 + {c_{2}}^2 }$$
Pythagoras' theorem
$$c_{1} = \sqrt{ {i}^2 - {c_{2}}^2 }$$
$$c_{2} = \sqrt{ {i}^2 - {c_{1}}^2 }$$
$$i : c_{1} = c_{1} : p_{1}$$
$$i : c_{2} = c_{2} : p_{2}$$
$$i : c_{2} = c_{2} : p_{2}$$
Isosceles Right Triangle
$$i = c \sqrt{2}$$
$$c = \frac{i}{\sqrt{2}}$$
$$A = \frac{{c}^2}{2}$$
$$A = \frac{{i}^2}{4}$$
$$c = \sqrt{2A}$$
Right Triangle 30 - 60°
$$i = c_{1} \times 2$$
Hypotenuse
$$c_{1} = \frac{i}{2}$$
Minimum Cathetus
$$c_{2} = c_{1} \sqrt{3}$$
Maximum Cathetus
$$c_{1} = \frac{c_{2}}{\sqrt{3}}$$
Minimum Cathetus
$$c_{2} = i \frac{\sqrt{3}}{2}$$
Maximum Cathetus
$$i = c_{2} \frac{2}{\sqrt{3}}$$
Hypotenuse
Definition
The right triangle is a triangle with a right angle (90 degree)
Properties
  1. It has a right angle (90 degree)
  2. The Pythagoras' theorem is valid
  3. All the  Generic Triangle formulas are valid
  4. It can be inscribed inside a semicircle where the radius is half the hypotenuse