Final answer:
In any triangle, angles and sides are ordered from smallest to largest based on their relative magnitudes. The smallest angle is opposite the shortest side, and the largest angle is opposite the longest side. Trigonometric ratios help in determining these relationships in a right-angled triangle.
Step-by-step explanation:
The question refers to the ordering of angles and sides of a triangle based on their magnitudes. In any triangle, the lengths of the sides and the measures of the angles are intimately related. The smallest angle is always opposite the shortest side, and the largest angle is opposite the longest side. By understanding the basic properties of triangles and the trigonometric ratios such as sine, cosine, and tangent, one can deduce the relative sizes of angles and sides.
For example, in a right triangle with sides 'x' and 'y' and hypotenuse 'h', where 'x' is the adjacent side and 'y' is the opposite side to one of the angles, the trigonometric ratios such as sine (y/h), cosine (x/h), and tangent (y/x) are used to relate angles to side lengths.
To order the angles and sides from smallest to largest in any given triangle, one would measure or calculate the angles using the appropriate relationships and order them accordingly, followed by aligning the lengths of the sides in the same order as their opposite angles.