Final answer:
A trigonometric ratio is a fraction representing the relationship between two sides of a right-angled triangle and includes sine, cosine, and tangent, which are key to understanding trigonometry.
Step-by-step explanation:
A trigonometric ratio is a simplified fraction of two sides of a right-angled triangle. Trigonometry focuses on the relationships between the angles and sides of right-angled triangles. These trigonometric ratios include sine, cosine, and tangent, which are fundamental to the field of trigonometry and are dimensionless, meaning they do not carry units.
For instance, for a given right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse, which is the longest side opposite the right angle. Similarly, the cosine of an angle is the ratio of the length of the adjacent side to the hypotenuse. Lastly, the tangent is the ratio of the length of the opposite side to the length of the adjacent side.
These ratios are often used to solve problems in various fields such as engineering, physics, and astronomy by helping to determine distances and angles within geometrical figures and in real-world applications.