A 30-60-90 triangle is a special type of right triangle where the three angles measure 30 degrees, 60 degrees, and 90 degrees. The sides have a specific relation because of the unique geometry of the triangle: the length of the side opposite the 30-degree angle is half the length of the hypotenuse and the length of the leg adjacent to the 30-degree angle is the factor larger than the opposite side.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the internal angles of a triangle in Euclidean space is always 180 degrees. The study of triangles is known as trigonometry.

A right triangle (or right-angled triangle) is a triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are known as the adjacent and opposite sides, relative to the non-right angle being referenced.

A 45-45-90 triangle is a special type of right triangle where the three angles measure 45 degrees, 45 degrees, and 90 degrees. The three angles describe a unique geometry where the hypotenuse is a factor √2 larger than the adjacent and opposite sides.