1. The problem is to understand the side length ratios in a 30°-60°-90° right triangle. 2. A 30°-60°-90° triangle is a special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. 3. The sides opposite these angles have consistent ratios: the side opposite 30° is the shortest, opposite 60° is medium length, and opposite 90° is the hypotenuse. 4. If we let the length of the side opposite the 30° angle be $x$, then: \[\text{Opposite 30°} = x\] 5. The side opposite the 60° angle is $x \sqrt{3}$ because it is longer by a factor of $\sqrt{3}$. \[\text{Opposite 60°} = x \sqrt{3}\] 6. The hypotenuse, opposite the 90° angle, is twice the shortest side: \[\text{Hypotenuse} = 2x\] 7. Therefore, the side length ratios are: \[1 : \sqrt{3} : 2\] which correspond to the sides opposite 30°, 60°, and 90° angles respectively. 8. This ratio helps in solving many geometry and trigonometry problems involving these triangles.