What Is Sine?

How the ratio is chosen

Because similar right triangles preserve the same angle-based side ratios, sine stays constant for a fixed acute angle even when the triangle is scaled larger or smaller.

This page keeps the chosen angle, the opposite side, and the hypotenuse visible together so sine is read from the geometry before it is treated as a trig function symbol.

For a 30-degree angle in a 30-60-90 triangle, the opposite side is half the hypotenuse, so sine is one half. The exact value comes from the triangle's structure; the calculator only reports a number after the correct sides have been named.

• Sine is the ratio of opposite side to hypotenuse in a right triangle.
• Sine is commonly remembered with SOH: opposite over hypotenuse.
• The hypotenuse is always the side opposite the right angle and is the longest side in the right triangle.
• Changing the size of a similar right triangle does not change the sine of the same acute angle.

Where sine helps

• Use sine when a right-triangle problem involves the opposite side and the hypotenuse relative to a chosen angle.
• Use it in geometry, trigonometry, and applied measurement problems involving heights or distances.
• Use sine as part of the SOH CAH TOA framework when deciding which trig ratio fits the data given.

Sine checks to make

• Do not identify opposite and adjacent without first fixing the reference angle.
• Do not use a non-right triangle with the basic SOH definition unless the problem has moved into broader trigonometry.
• Do not confuse the hypotenuse with whichever side happens to look longest in a rough sketch; it must be opposite the right angle.