stylistic:style_transfer, information:filtering, information:highlighting, structural:summarization
Right-angled triangle definition

To define the sine and cosine of an acute angle α {\displaystyle \alpha }, start with a right triangle that contains an angle of measure α {\displaystyle \alpha }; in the accompanying figure, angle α {\displaystyle \alpha } in a right triangle A B C {\displaystyle ABC} is the angle of interest. The three sides of the triangle are named as follows:

Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side divided by the length of the hypotenuse, and the cosine of the angle is equal to the length of the adjacent side divided by the length of the hypotenuse: sin (α) = opposite hypotenuse, cos (α) = adjacent hypotenuse. {\displaystyle \sin(\alpha)={\frac {\text{opposite}}{\text{hypotenuse}}},\qquad \cos(\alpha)={\frac {\text{adjacent}}{\text{hypotenuse}}}.}