https://wikimd.com/index.php?action=history&feed=atom&title=Right_triangleRight triangle - Revision history2026-04-22T10:31:12ZRevision history for this page on the wikiMediaWiki 1.44.2https://wikimd.com/index.php?title=Right_triangle&diff=5644585&oldid=prevPrab: CSV import2024-04-22T04:40:32Z<p>CSV import</p>
<p><b>New page</b></p><div>[[File:Rtriangle.svg|Rtriangle|thumb]] [[File:Illustration_to_Euclid's_proof_of_the_Pythagorean_theorem2.svg|Illustration to Euclid's proof of the Pythagorean theorem2|thumb|left]] [[Image:Teorema.png|Teorema|thumb|left]] [[Image:thm_mediane.svg|thm mediane|thumb]] '''Right triangle''' or '''right-angled triangle''' is a [[triangle]] in which one of the angles is a [[right angle]] (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for [[trigonometry]].<br />
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The side opposite the right angle is called the [[hypotenuse]] (side ''c'' in the figure below). The sides adjacent to the right angle are called the [[legs]] (sides ''a'' and ''b'' in the figure below).<br />
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==Properties and formulas==<br />
A right triangle has several important properties and formulas:<br />
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* The [[Pythagorean theorem]] states that in a right triangle, the square of the length of the hypotenuse (''c'') is equal to the sum of the squares of the lengths of the legs (''a'' and ''b''): ''a''² + ''b''² = ''c''².<br />
* The [[trigonometric functions]] ([[sine]], [[cosine]], and [[tangent]]) can be defined in the context of a right triangle. For an angle θ:<br />
** The sine of θ is the ratio of the length of the opposite leg to the length of the hypotenuse.<br />
** The cosine of θ is the ratio of the length of the adjacent leg to the length of the hypotenuse.<br />
** The tangent of θ is the ratio of the length of the opposite leg to the length of the adjacent leg.<br />
* The [[area]] of a right triangle can be found using the formula: 1/2 * base * height, where the base and height are the lengths of the two legs.<br />
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==Special right triangles==<br />
There are two special types of right triangles:<br />
* A '''45°-45°-90° triangle''', where the legs are of equal length and the hypotenuse is √2 times the length of a leg.<br />
* A '''30°-60°-90° triangle''', where the lengths of the sides are in the ratio 1:√3:2, respectively.<br />
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==Applications==<br />
Right triangles are used in various fields such as [[engineering]], [[architecture]], and [[physics]], where the principles of [[trigonometry]] are applied to solve problems involving distances, angles, and heights.<br />
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==See also==<br />
* [[Triangle]]<br />
* [[Trigonometry]]<br />
* [[Pythagorean theorem]]<br />
* [[Special right triangles]]<br />
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[[Category:Geometry]]<br />
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