To find the missing side length AB in the right triangle using the tangent ratio, we will use the relationship defined by the tangent of an angle in a right triangle:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, side AC is the angle \(26^\circ\), side BC (15) is the side adjacent to angle A, and side AB is the opposite side that we want to find. Therefore, we can set up the equation as follows:
\[ \tan(26^\circ) = \frac{\text{AB}}{BC} \]
Substituting the known values:
\[ \tan(26^\circ) = \frac{\text{AB}}{15} \]
Now, we need to find \(\tan(26^\circ)\). Using a calculator, we find:
\[ \tan(26^\circ) \approx 0.4877 \]
Now we can substitute this back into our equation:
\[ 0.4877 = \frac{\text{AB}}{15} \]
To solve for AB, multiply both sides by 15:
\[ \text{AB} = 15 \times 0.4877 \approx 7.315 \]
Looking at the answer choices, the closest value is approximately:
\[ \text{AB} \approx 7.32 \]
So the correct answer is:
A. side AB = 7.32