An obtuse triangle is a type of polygon with three sides and three angles, one of which is greater than 90 degrees and less than 180 degrees. This type of triangle is the opposite of an acute triangle, which has all angles less than 90 degrees, and a right triangle, which has one angle equal to 90 degrees. Obtuse triangles can be classified as scalene, isosceles, or equilateral depending on the lengths of their sides. In an isosceles obtuse triangle, two sides are equal in length, and the third is longer; in an equilateral obtuse triangle, all sides are equal in length. One important characteristic of an obtuse triangle is that it cannot be inscribed in a circle. This is because the angle opposite the longest side, which is the obtuse angle, is too large to fit inside a circle. Additionally, the altitude of an obtuse triangle is located outside of the triangle itself, unlike in an acute or right triangle where the altitude is located inside the triangle. Obtuse triangles can be used in real-world applications such as architecture, engineering, and physics. For example, in architecture, obtuse triangles can be used to construct roofs with a steep pitch. In engineering, obtuse triangles can be used to calculate the forces acting on a structure. In physics, obtuse triangles can be used to calculate the trajectory of a projectile. In summary, an obtuse triangle is a type of polygon with one angle greater than 90 degrees and less than 180 degrees. It can be classified as scalene, isosceles, or equilateral depending on the lengths of its sides. Obtuse triangles cannot be inscribed in a circle, and their altitude is located outside of the triangle. They have practical applications in fields such as architecture, engineering, and physics.
polygon, acute triangle, right triangle, scalene, isosceles, equilateral, inscribed, altitude, architecture, engineering, physics
An obtuse triangle is a polygon with three sides and three angles, two of which are acute angles, and one of which is an obtuse angle. This obtuse angle is greater than 90 degrees and less than 180 degrees. Obtuse triangles are classified as scalene, isosceles, or equilateral depending on the lengths of their sides. In an isosceles obtuse triangle, two sides are equal in length, and the third is longer; in an equilateral obtuse triangle, all sides are equal in length. As a mathematician, the study of obtuse triangles is especially interesting due to the fact that they can have a wide range of properties and characteristics, depending on the measurements of the sides and angles.
Vertex, angle bisector, median, hypotenuse, circumcircle.
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