Final answer:
The ratio for sin A is Ay/A, where Ay is the length of the side opposite to angle A and A is the hypotenuse. The ratio for cos A is Ax/A, where Ax is the length of the side adjacent to angle A and A is the hypotenuse.
Step-by-step explanation:
To write the ratios for sin A and cos A, we refer to a right-angled triangle where angle A is one of the two non-right angles. The ratio for sin A (θ) is given by the length of the side opposite angle A (often labeled as Ay in diagrams) divided by the length of the hypotenuse (labeled as A). This can be represented as sin A = Ay/A. Similarly, the ratio for cos A (θ) is determined by dividing the length of the side adjacent to angle A (Ax) by the hypotenuse (A) and is represented as cos A = Ax/A. In vector analysis, these ratios help in finding scalar components of vectors when the magnitude and direction are known.