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HandWiki. Right Triangle. Encyclopedia. Available online: https://encyclopedia.pub/entry/29612 (accessed on 14 October 2026).
HandWiki. Right Triangle. Encyclopedia. Available at: https://encyclopedia.pub/entry/29612. Accessed October 14, 2026.
HandWiki. "Right Triangle" Encyclopedia, https://encyclopedia.pub/entry/29612 (accessed October 14, 2026).
HandWiki. (2022, October 17). Right Triangle. In Encyclopedia. https://encyclopedia.pub/entry/29612
HandWiki. "Right Triangle." Encyclopedia. Web. 17 October, 2022.
Right Triangle
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The content is sourced from: https://handwiki.org/wiki/Right_triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle 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. The side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B. If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.

right-angled triangle trigonometry triangle

References

  1. Di Domenico, Angelo S., "A property of triangles involving area", Mathematical Gazette 87, July 2003, pp. 323-324.
  2. Posamentier, Alfred S., and Salkind, Charles T. Challenging Problems in Geometry, Dover, 1996.
  3. Wentworth p. 156
  4. Voles, Roger, "Integer solutions of [math]\displaystyle{ a^{-2} + b^{-2} = d^{-2} }[/math]," Mathematical Gazette 83, July 1999, 269–271.
  5. Richinick, Jennifer, "The upside-down Pythagorean Theorem," Mathematical Gazette 92, July 2008, 313–317.
  6. Inequalities proposed in “Crux Mathematicorum”, [1].
  7. Triangle right iff s = 2R + r, Art of problem solving, 2011 http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=411120
  8. Andreescu, Titu and Andrica, Dorian, "Complex Numbers from A to...Z", Birkhäuser, 2006, pp. 109-110.
  9. Properties of Right Triangles http://www.ricksmath.com/right-triangles.html
  10. CTK Wiki Math, A Variant of the Pythagorean Theorem, 2011, [2].
  11. Darvasi, Gyula (March 2005), "Converse of a Property of Right Triangles", The Mathematical Gazette 89 (514): 72–76 .
  12. Bell, Amy (2006), "Hansen's Right Triangle Theorem, Its Converse and a Generalization", Forum Geometricorum 6: 335–342, http://forumgeom.fau.edu/FG2006volume6/FG200639.pdf 
  13. Di Domenico, A., "The golden ratio — the right triangle — and the arithmetic, geometric, and harmonic means," Mathematical Gazette 89, July 2005, 261. Also Mitchell, Douglas W., "Feedback on 89.41", vol 90, March 2006, 153-154.
  14. Posamentier, Alfred S., and Lehmann, Ingmar. The Secrets of Triangles. Prometheus Books, 2012.
  15. Bailey, Herbert, and DeTemple, Duane, "Squares inscribed in angles and triangles", Mathematics Magazine 71(4), 1998, 278-284.
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