Which of the following correctly defines the sine ratio?

Study for the HSC Mathematics Standard 2 Exam. Utilize flashcards and multiple choice questions, each with hints and explanations. Prepare confidently for your exam success!

The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. This means that if you have a right triangle and you are interested in one of the acute angles, the sine of that angle can be found by taking the length of the opposite side and dividing it by the length of the hypotenuse.

In the context of the choices provided, the correct definition of sine is represented by the option that states the ratio is the length of the opposite side (O) over the hypotenuse (H). Thus, this option reflects the fundamental definition of the sine function in trigonometry, making it essential for solving problems involving right triangles.

The other options either mix up the sides in relation to the angle or do not adhere to the traditional definitions of trigonometric ratios, which is why they do not correctly define the sine function. Understanding this concept is vital for anyone studying trigonometry, as it forms the basis for solving a wide range of real-world problems.

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