Final answer:
The value of tan(A) in a right triangle ABC is the ratio of the length of the opposite side to the length of the adjacent side. Without specific side lengths given, we cannot find the exact value of tan(A). However, by assuming the sides are 5 and 12 from the reference example, the value is 12/5.
Step-by-step explanation:
To find the value of tan(A) for a right triangle ABC, we need to look at the sides of the triangle. According to the definitions of trigonometric functions for right triangles, tangent of angle A, or tan(A), is the ratio of the length of the opposite side to angle A to the length of the adjacent side to angle A. In other words, if we label the opposite side as Ay and the adjacent side as Ax, then tan(A) = Ay/Ax.
In the provided reference information, there is mention of the Pythagorean theorem, which is essential for understanding right triangles. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (x² + y² = h²). However, without knowledge of the specific lengths of the sides of triangle ABC, we cannot determine the exact value of tan(A) just from the reference provided.
If we assume sides Ax and Ay correspond to the sides with lengths 5 and 12 (from the previous example in the references), respectively, then using the tangent function, tan(A) = 12/5, which corresponds to choice C from the given options.