A right triangle is a triangle with one right angle, an angle of exactly 90 degrees. The two sides that form the right angle are the legs, and the longest side, across from the right angle, is the hypotenuse. Its sides follow the Pythagorean theorem: a2 + b2 = c2.
The legs meet at the right angle; the hypotenuse faces it. 36 + 64 = 100, so c = 10.
Formal definition and notation
A right triangle is a triangle ABC in which one interior angle, say ∠ C, measures 90°. The sidesa and b adjacent to ∠ C are the legs and the side c opposite it is the hypotenuse. Then a2 + b2 = c2, the other two angles are acute and complementary, and the area is 12ab.
The hypotenuse is one side of a right triangle: the longest one, across from the right angle.
Quick check: 3 questions
Question 1 of 3
The legs of a right triangle are 6 and 8. What is the hypotenuse?
Show answer and explanation
Answer: C.√36 + 64 = √100 = 10. Choice A adds the legs, B forgets the square root, and D multiplies the legs.
Question 2 of 3
A right triangle has legs of 5 m and 12 m. What is its area?
Show answer and explanation
Answer: A.12 × 5 × 12 = 30. Choice B forgets the one half, C adds the legs, and D uses the hypotenuse 13 with a leg.
Question 3 of 3
One acute angle of a right triangle is 35°. What is the other acute angle?
Show answer and explanation
Answer: B. The acute angles add to 90°: 90 − 35 = 55. A subtracts from 180, C assumes the angles match, and D subtracts from 100.
Right Triangle: frequently asked questions
How do you know if a triangle is a right triangle?
Look for a right-angle mark or a 90° angle. If you only know the three sides, test them: square the two shorter sides and add. If the sum equals the square of the longest side, it is a right triangle. Sides 7, 24 and 25 pass, because 49 + 576 = 625.
Can a right triangle be isosceles?
Yes. If the two legs are equal, the triangle is an isosceles right triangle, and its acute angles are both 45 degrees. A square cut along its diagonal makes two of them. A right triangle can never be equilateral, though, because an equilateral triangle has three 60-degree angles.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.G.A.2, CCSS 8.G.B.7
Cite this entry
Effortless Math Team. “Right Triangle.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/right-triangle/
Flashcard
TermRight Triangleone 90° angle
DefinitionA triangle with a right angle; the legs form it and the hypotenuse faces it. Legs 6 and 8 give hypotenuse 10.
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