Answer :
To determine which basic trigonometric ratio compares the side opposite an angle to the hypotenuse, let's review the definitions of each trigonometric function:
1. Arccosine: This is the inverse function of the cosine. It returns the angle whose cosine is a given number.
2. Arctangent: This is the inverse function of the tangent. It returns the angle whose tangent is a given number.
3. Cosine: Cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.
4. Sine: Sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
From these definitions, we can see that the trigonometric function that directly compares the side opposite an angle to the hypotenuse is the Sine function.
Thus, the correct answer is:
Sine
1. Arccosine: This is the inverse function of the cosine. It returns the angle whose cosine is a given number.
2. Arctangent: This is the inverse function of the tangent. It returns the angle whose tangent is a given number.
3. Cosine: Cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.
4. Sine: Sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
From these definitions, we can see that the trigonometric function that directly compares the side opposite an angle to the hypotenuse is the Sine function.
Thus, the correct answer is:
Sine