Basic Elements of a Right Triangle
In a right triangle, different elements can be distinguished, referring to its sides and angles.
- Legs (or cathetus): are the sides of the triangle that together form the right angle.
- Hypotenuse: is the largest side of the triangle opposite the right angle.
- Right angle: is a 90° angle formed by the two legs.
- Acute angles: the other two angles of the triangle (α and β) are less than 90°.
Download this calculator to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.
Triangle-total.rar or Triangle-total.exe
Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.
Relationship between Legs and Hypotenuse
Pythagorean Theorem
The Pythagorean theorem, also known as Pythagoras’s theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle (2 legs and hypotenuse). This theorem can be written as the following equation:
Geometric Mean Theorem
The Geometric mean theorem (or Altitude-on-Hypotenuse Theorem) relates the height (h) of the triangle and the legs of two triangles similar to the main ABC, by plotting the height h over the hypotenuse, stating that in every right triangle, the height (h) relative to the hypotenuse is the geometric mean of the two projections of the legs on the hypotenuse (n and m).
Leg Rule
The leg rule is a theorem that relates the segments projected by the legs on the hypotenuse with the legs they touch.
In every right triangle, a leg (a or b) is the geometric mean between the hypotenuse (c) and the projection of that leg on it (n or m).