To find tan J, one must know the lengths of the opposite and adjacent sides of angle J in a right triangle. Without this data, we cannot provide tan J as a fraction in simplest form. If we had the side lengths, tan J equals the opposite side divided by the adjacent side, which we then simplify.
To express tan J as a fraction in simplest form, we would need additional information, specifically the values of the opposite side and the adjacent side from a right triangle where J is one of the angles. The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side (tan J = opposite/adjacent). Without this specific information, we cannot provide an exact fraction.
As an example, let's assume that in a right triangle, the length of the side opposite angle J is 15 units and the length of the adjacent side to angle J is 20 units. Using these values, tan J would be 15/20. By simplifying this fraction, we would divide both numerator and denominator by their greatest common divisor, which is 5. Therefore, tan J = 15/20 simplifies to 3/4.
Remember that the simplest form of a fraction is achieved when the numerator and denominator are as small as possible and have no common factors other than 1.