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Naming the sides

Now that we know the ratios are constant, we can name the sides.

In order to distinguish the various possible ratios in a right-angled triangle, we introduce some names. We always refer to the longest side (opposite the right-angle) as the hypotenuse.

We now choose one of the two acute angles and label it, often using one of the Greek letters α, β, γ or θ. We shall call this angle the reference angle.

The side opposite the reference angle is called the opposite side, generally referred to as the opposite, and the remaining side is called the adjacent side, or simply adjacent, since it is next to the reference angle.

Right-angled triangle ABC.
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