A 30-60-90 triangle is a special type of right triangle characterized by its angles measuring 30 degrees, 60 degrees, and 90 degrees. The unique angle measures create a consistent ratio between the lengths of the sides. In this triangle, the side opposite the 30-degree angle is the shortest, the side opposite the 60-degree angle is longer, and the hypotenuse, opposite the 90-degree angle, is the longest. The side lengths of a 30-60-90 triangle follow a specific ratio: 1 : √3 : 2. This means if the shortest side (opposite the 30-degree angle) is 1 unit, the longer side (opposite the 60-degree angle) will be √3 units, and the hypotenuse will be 2 units. This predictable relationship makes it easy to solve problems involving these triangles.