Which trigonometric ratio represents the opposite side divided by the hypotenuse in a right triangle?
Sine
We are given a question regarding the trigonometric ratio in a right triangle that represents the opposite side divided by the hypotenuse. Let's solve this step-by-step:
Explanation of Trigonometric Ratios in a Right Triangle:
- In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
- This relationship is given by the formula: \(\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}\)
- The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse: \(\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}\)
- The tangent of an angle is the ratio of the length of the opposite side to the adjacent side: \(\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}\)
- The cotangent is the reciprocal of the tangent: \(\cot(\theta) = \frac{\text{Adjacent}}{\text{Opposite}}\)
From the above definitions, it is clear that the trigonometric ratio that represents the opposite side divided by the hypotenuse is Sine (\(\sin\)).
Conclusion:
The correct answer is Sine, as it accurately describes the ratio of the opposite side to the hypotenuse in a right triangle.
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