Final answer:
Without specific measurements of the sides or angles of the triangle, it is impossible to determine the exact values of sin(x) and tan(y). Assuming a 3-4-5 right triangle, the values would be sin(x) = 4/5 and tan(y) = 3/4, but this is not conclusive without additional information.
Step-by-step explanation:
To solve the mathematical problem completely and find the values of sin(x) and tan(y) in the given triangle, we need additional information about the sides of the triangle. In a right triangle, sin(x) can be defined as the ratio of the length of the side opposite to angle x to the length of the hypotenuse of the triangle, and tan(y) can be defined as the ratio of the length of the side opposite to angle y to the length of the side adjacent to angle y. Without the actual measures of the sides or angles provided in the question, it is not possible to determine the exact values of sin(x) and tan(y).
However, if we assume a right triangle with sides of length 3, 4, and 5, where 5 is the hypotenuse, then sin(x) would be 4/5 if x is opposite the side of length 4, and tan(y) would be 3/4 if y is the angle opposite the side of length 3. This corresponds to option (a) sin(x) = 4/5, tan(y) = 3/4. Without more information, though, we cannot conclusively determine the correct option answer in the final answer.
To conclude the complete answer, additional details about the triangle are required. The relevant formulas used for such calculations include the sine and cosine functions, the Law of Sines, and the Law of Cosines, all of which relate the angles of a triangle to its side lengths