What is the relationship expressed by the sine ratio in a right triangle?

In a right triangle, the sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. This relationship can be derived from the basic trigonometric definitions.

When you have a right triangle, one of the angles is 90 degrees, and the sine of an angle (other than the right angle) is calculated by taking the length of the side that is directly opposite that angle and dividing it by the length of the hypotenuse, which is the longest side of the triangle. Therefore, if you label the sides of the triangle, the sine ratio can be expressed as:

[

\text{sine(angle)} = \frac{\text{Opposite}}{\text{Hypotenuse}}

]

This key relationship is fundamental in trigonometry and is used in various applications such as solving for unknown side lengths or angles in right triangles. This clear definition is why the answer is correct.