The sine of an acute angle is the ratio of which sides?

The sine of an acute angle is the ratio of which sides?

• A. adjacent/opposite
• B. opposite/hypotenuse
• C. hypotenuse/opposite
• D. opposite/adjacent

Answer: (B)

Sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In a right triangle, the hypotenuse is the longest side, opposite the right angle, so sin(angle) equals opposite over hypotenuse. This makes the sine value depend only on the angle, not the triangle’s size. For reference, cosine uses adjacent over hypotenuse, and tangent uses opposite over adjacent; the remaining ratios (hypotenuse over opposite) would be the reciprocal of sine, known as cosecant. For example, if the opposite side is 3 and the hypotenuse is 5, sin(angle) = 3/5 = 0.6.

Sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In a right triangle, the hypotenuse is the longest side, opposite the right angle, so sin(angle) equals opposite over hypotenuse. This makes the sine value depend only on the angle, not the triangle’s size. For reference, cosine uses adjacent over hypotenuse, and tangent uses opposite over adjacent; the remaining ratios (hypotenuse over opposite) would be the reciprocal of sine, known as cosecant. For example, if the opposite side is 3 and the hypotenuse is 5, sin(angle) = 3/5 = 0.6.