In a 30° and 60° triangle, what is the ratio of the lengths of the opposite side to the hypotenuse for the 30° angle?

In a 30° and 60° triangle, which is a specific type of right triangle, the angles and the relationships between the sides have unique properties. The side opposite the 30° angle is specifically known to be half the length of the hypotenuse.

To understand this ratio, consider a right triangle where the hypotenuse is assigned a length of 1 unit. In this case, the side opposite the 30° angle will measure exactly half of that length, which is 0.5 units. Therefore, if we express the ratio of the length of the opposite side (0.5) to the length of the hypotenuse (1), we simplify this ratio as follows:

0.5 : 1 can be expressed as 1 : 2 when both sides of the ratio are multiplied by 2 to eliminate the decimal.

Thus, the correct answer is indeed 1:2, reflecting the established properties of the sides in a 30-60-90 triangle. Understanding these ratios is critical in solving problems involving right triangles and trigonometric functions.