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How do the labels opposite, adjacent, and hypotenuse depend on the chosen angle in a right triangle?

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Diagram of a right triangle labeled with sides a, b, and hypotenuse c, alongside formulas for the six trigonometric functions-sine, cosine, tangent, cosecant, secant, and cotangent-each defined by ratios of the triangle's sides. — trigonometry Based on the definitions, various simple relationships exist among the functions. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

In a right triangle, the labels "opposite," "adjacent," and "hypotenuse" are defined relative to one of the two acute angles being considered.12

Hypotenuse: This is always the longest side of the triangle, located directly opposite the 90-degree angle. Its identity does not change regardless of which acute angle you choose.12
Opposite: This is the side located directly across from the specific acute angle you are referencing.12
Adjacent: This is the side that helps form the chosen acute angle (other than the hypotenuse). It is the side "next to" the angle.12

Because these labels depend on the chosen angle, the "opposite" side for one acute angle becomes the "adjacent" side for the other acute angle, and vice versa. These relationships are fundamental to defining trigonometric functions such as sine, cosine, and tangent, which express the ratios between these sides.12