1. **Problem Statement:** We have a right triangle TUS with a right angle at U, angle at S measuring 59°, and side TU opposite angle S with length 7 units. We need to find the length of side SU. 2. **Identify the sides:** In triangle TUS, - Angle at S = 59° - Right angle at U = 90° - Side TU = 7 (opposite angle S) - Side SU is adjacent to angle S 3. **Formula used:** For a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Apply the formula:** Here, angle $\theta = 59^\circ$, opposite side = TU = 7, adjacent side = SU (unknown). $$\tan(59^\circ) = \frac{7}{SU}$$ 5. **Solve for SU:** $$SU = \frac{7}{\tan(59^\circ)}$$ 6. **Calculate the value:** Using a calculator, $$\tan(59^\circ) \approx 1.6643$$ So, $$SU = \frac{7}{1.6643} \approx 4.204$$ 7. **Final answer:** Rounded to the nearest tenth, $$SU \approx 4.2$$ units. Thus, the length of side SU is approximately 4.2 units.