What are sine, cosine and tangent in a right triangle?

What sine, cosine and tangent mean in a right triangle: opposite, adjacent and hypotenuse, the three ratios, and the SOH CAH TOA memory trick.

Step-by-step explanation

1. In a right-angled triangle, we define the sides relative to an angle theta. The side opposite the angle is called the 'Opposite', the side next to it is the 'Adjacent', and the longest side is the 'Hypotenuse'.
2. The Sine of theta is the ratio of the length of the Opposite side to the Hypotenuse.
3. The Cosine of theta is the ratio of the length of the Adjacent side to the Hypotenuse.
4. The Tangent of theta is the ratio of the length of the Opposite side to the Adjacent side.
5. A common mnemonic to remember these ratios is SOH CAH TOA: Sine is Opposite/Hypotenuse, Cosine is Adjacent/Hypotenuse, and Tangent is Opposite/Adjacent.

This is a real answer from Math Motion AI: the explanation and the animation were made by the site for this question.

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