If a right triangle is inscribed in a circle, one of its sides (the hypotenuse) is a diameter of the circle. Trigonometric functions are often defined in terms of right triangles as: In trigonometry, the legs of a right triangle are often referred to as the opposite side and the adjacent side of their respective acute angle, θ, as shown in the figure below. Right triangles are widely used in trigonometry. There are many sets of Pythagorean triples. So, the Pythagorean Theorem is satisfied and 3-4-5 is a set of Pythagorean triples. Also, if the side lengths of a right triangle are all integers, they are a set of Pythagorean triples.įor example, if a = 3, b = 4, and c = 5, then: If a triangle has side lengths such that the set of sides comprise a Pythagorean triple, the triangle is a right triangle. The sets of positive integers that satisfy the Pythagorean Theorem equation are called Pythagorean triples. Where a and b are the lengths of the two legs, and c is the length of the hypotenuse of the right triangle. The theorem shows a distinct relationship between the sides of a right triangle which can be expressed as: The Pythagorean Theorem, named after the Greek mathematician Pythagoras, is one of the more well-known theorems in mathematics. Right triangles and the Pythagorean Theorem

Otherwise, the shape cannot be a triangle. Since the measure of a right angle is 90°, and since the sum of the three angles in any triangle equals 180°, the sum of the other two angles in a right triangle must be 180° - 90° = 90°, so they must be acute angles. The hypotenuse is the longest side of the right triangle.

The sides that form the right angle are called legs. The side opposite the right angle of a right triangle is called the hypotenuse. Right angles are typically denoted by a square drawn at the vertex of the angle that is a right angle. Home / geometry / triangle / right triangle Right triangleĪ right triangle is a triangle in which one angle has a measurement of 90° (a right angle), such as the triangle shown below.

Isosceles right triangle equation