- angle
- atan2
- buttress
- Cathetus
- folk etymology
- geometry
- grammatical gender
- Latin
- Nonhypotenuse number
- participle
- polar coordinates
- present tense
- Pythagorean theorem
- right angle
- Right triangle
- Space diagonal
- Square (algebra)
- square root
- Taxicab geometry
- Triangle
- Trigonometry
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For example, if one of the other sides has a length of 3 meters (when squared, 9 m²) and the other has a length of 4 m (when squared, 16 m²), then their squares add up to 25 m². The length of the hypotenuse is the square root of this, or 5 m.
Etymology
The word hypotenuse derives from Latin hypotēnūsa, a transliteration of Ancient Greek , the feminine present participle of hypoteínō, a combination of hypó ("under") and teínō ("I stretch"). The word ὑποτείνουσα was used for the hypotenuse of a triangle by Plato in the Timeus 54d and by many other ancient authors.A folk etymology says that tenuse means "side", so hypotenuse means a support like a prop or buttress, but this is inaccurate.
Calculating the hypotenuse
Usually the length of the hypotenuse is calculated using the square root function derived from the Pythagorean theorem. Setting x = c1 and y = c2 to avoid subscripts:
In mathematical notation;
:
Many computer languages support the ISO C standard function hypot(x,y), which returns the value above. The function is designed not to fail where the straightforward calculation might overflow or underflow and can be slightly more accurate.
Some scientific calculators provide a function to convert from rectangular coordinates to polar coordinates. This gives both the length of the hypotenuse and the angle the hypotenuse makes with the base line (c1 above) at the same time when given x and y. The angle returned will normally be that given by atan2(y,x).
Properties
::b² = a · m ::c² = a · n
::a/b = b/m ::a/c = c/n
Trigonometric rates
By means of trigonometric rates, can obtain the value of two acute angles, and , of the right triangle.Known the length of the hypotenuse and of the a cathetiy , the rate between both is:
:::
Therefore, the trigonometric inverse function is:
::: In which is the value of the opposite of the catheti .
The adjoining angle of the catheti , will be = 90º –
Also, can obtain the value of the angle thru the equation:
:::
In which is the other catheti.
See also
Notes
References
Category:Elementary geometry Category:Triangles Category:Trigonometry
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