Final answer:
The side of length x opposite angle a in a right triangle corresponds to the sine (sin) ratio, which is the correct option for this relationship.
Step-by-step explanation:
When considering a right triangle, the side of length x opposite angle a is related to the angle through the trigonometric ratio called the sine (sin). The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, if you know the length of the opposite side (y) and the hypotenuse (h), you can calculate sin(a) as y/h. Additionally, other trigonometric ratios such as cosine and tangent can also be used in right triangles.
In the cosine function, it is the ratio of the length of the adjacent side (x) to the hypotenuse (h), which is calculated as x/h. Similarly, the tangent function relates the length of the opposite side to the adjacent side, calculated as y/x. The Pythagorean theorem, which states a² + b² = c², helps to find relationships between the sides of a right triangle. However, for angle a and side x, the sine ratio is the relevant trigonometric ratio. The answer to the student's question is (a) Sine (sin), making it the correct option for the relationship between a side of length x opposite angle a in a right triangle.