1. **State the problem:** We have a right triangle ABC with angle C = 90 degrees, hypotenuse AB = 39, adjacent side AC = 36, and opposite side BC = 15. We need to find $\tan A$. 2. **Recall the definition of tangent:** For an angle in a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. 3. **Identify opposite and adjacent sides for angle A:** - Opposite side to angle A is BC = 15. - Adjacent side to angle A is AC = 36. 4. **Calculate $\tan A$:** $$\tan A = \frac{BC}{AC} = \frac{15}{36}$$ 5. **Simplify the fraction:** $$\frac{15}{36} = \frac{\cancel{3}5}{\cancel{3}12} = \frac{5}{12}$$ 6. **Final answer:** $$\tan A = \frac{5}{12}$$ This corresponds to option c.