Hypotenuse
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The hypotenuse of a right triangle (or right-angled triangle) is the side opposite its right angle. It is the longest side of a right triangle.
We can find the hypotenuse of a triangle using the Pythagorean Theorem if we know the length of the two legs (a and b). The formula is:
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.
Exercise
Find the hypotenuse of the triangle shown below:
We apply the equation:
So the hypotenuse is 5 cm.
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).
AUTHOR: Bernat Requena Serra
YEAR: 2020