Cathetus
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- This page is about the geometric meaning. For the plant, see Phyllanthus. For the epiplemiine moth, see Monobolodes.
In a right triangle, the cathetus (From the Greek word "Κάθετος", plural, catheti Greek: "Κάθετοι") is either one of the two sides which are adjacent to the right angle. The remaining side, opposite the right angle, is called the hypotenuse. The cathetus is far more frequently known as a "leg" of the right triangle, or by the periphrasis "side about the right angle". When they are related to the hypotenuse, the catheti are often referred to simply as "the other two sides".
The ratio of the lengths of the catheti defines the trigonometric functions tangent and cotangent of the angles in the triangle. In a right triangle, the length of the cathetus is also the geometric mean between the length of the segment cut by the altitude to the hypotenuse and the length of the whole hypotenuse.
If a right triangle is not isosceles (i.e. it is scalene), then its catheti have different lengths and a distinction can be made between the "minor" one and the "major" one.
In an isosceles triangle, the cathetus of the triangle are the two congruent sides of the triangle.
By the Pythagorean theorem, the sum of the areas of the squares on the catheti is equal to the area of the square on the hypotenuse. Equivalently, the sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse.
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[edit] Generally
In a wider sense, a cathetus is any line falling perpendicularly on another line or a surface. Such a line is more commonly known as a surface normal.
[edit] References
- Bernhardsen, T. Geographic Information Systems: An Introduction, 3rd ed. New York: Wiley, p. 271, 2002.
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