Right triangle
A triangle with one 90-degree angle. Its side opposite that angle, called the hypotenuse, is longer than either other side.
Pythagorean theorem: A theorem stating that the square of a right triangle’s hypotenuse equals the sum of the squares of its legs. It gives the defining length relationship among the triangle’s three sides.
Triangle: A polygon with three sides, three vertices, and three interior angles. A right triangle is a specific kind of triangle distinguished by one angle.
45-45-90 triangle: An isosceles right triangle whose angles are 45, 45, and 90 degrees. Equal legs make this the simplest symmetric right-triangle case.
Surveying: The measurement and mapping of land, boundaries, and locations using geometric and instrumental methods. Surveyors use right-triangle relationships to infer inaccessible distances and heights.
Oblique triangle: A triangle with no right angle; its angles are all acute or one is obtuse. It lacks the defining 90-degree angle and requires different side-solving relationships.
Trigonometric functions: Functions relating angles to ratios of side lengths in triangles and to coordinates on the unit circle. Sine, cosine, and tangent encode ratios of this triangle’s sides.
Angle: A figure formed by two rays sharing an endpoint, or the amount of rotation between them. The 90-degree angle is the feature that defines this triangle.
30-60-90 triangle: A right triangle with angles of 30, 60, and 90 degrees, whose side lengths follow a fixed ratio. Its fixed side ratio makes exact trigonometric values easy to derive.
Triangulation: A method of locating a point by measuring angles from known positions. Right-triangle geometry can convert measured angles and baselines into distances.
Acute triangle: A triangle whose three interior angles are each less than 90 degrees. Unlike a right triangle, none of its angles is 90 degrees.