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Right Triangle
right - upright or 'perfect'
A triangle where one of its interior angles is a right angle (90 degrees).
Try this Drag the orange dots on each vertex to reshape the triangle. Notice it always remains a right triangle, because the angle ∠ABC is always 90 degrees.
(If there is no image below, see support page.)
Right triangles figure prominently in various branches of mathematics. For example, trigonometry concerns itself almost exclusively with the properties of right triangles, and the famous theorem by Pythagoras defines the relationship between the three sides of a right triangle:
a2 + b2 = h2
where h  is the length of the hypotenuse
a,b  are the lengths of the the other two sides
Attributes
Hypotenuse The side opposite the right angle. This will always be the longest side of a right triangle.
Sides The two sides that are not the hypotenuse. They are the two sides making up the right angle itself.
Properties
  • A right triangle can also be isosceles if the two sides that include the right angle are equal in length (AB and BC in the figure above)
  • A right triangle can never be equilateral, since the hypotenuse (the side opposite the right angle) is always longer than the other two sides.
Things to Ponder
Can a right triangle also be isosceles? answer Yes, if its sides have the same length. In the diagram above, try to create such a triangle
Can a right triangle also be a scalene triangle? answer Yes, if the two sides have different length. The hypotenuse is always the longest side, so it must be a different length to the sides
One angle of a right triangle is 41°. What are the other two? answer 49° and 90°. The interior angles of any triangle always add up to 180°
What is the area of a right triangle with sides of length 12 and 15cm? answer Somewhere between 89 and 94 square cm
A right triangle has a hypotenuse 10 meters long, and one leg 6 meters long. What is the length of the other leg? answer Somewhere between 7.1 and 8.9 meters

Related triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises

(C) 2009 Copyright John Page