1. **Problem statement:** We have points R, S, and T on horizontal ground with RS = 9.8 m and ST = 13.5 m. A vertical flagpole RQ stands at R. The angle of depression from Q to S is 37°. S is due south of R, and the bearing of T from S is 052°. We need to find the length of RQ. 2. **Understanding the problem:** The angle of depression from Q to S is the angle between the horizontal line through Q and the line QS. Since Q is vertically above R, the horizontal through Q is parallel to the ground. 3. **Key formula:** The angle of depression equals the angle of elevation from S to Q. We can use right triangle RSQ where RQ is vertical, RS is horizontal, and angle at Q is 37°. 4. **Using trigonometry:** In right triangle RSQ, - $\tan(37^\circ) = \frac{RQ}{RS}$ 5. **Calculate RQ:** $$ RQ = RS \times \tan(37^\circ) = 9.8 \times \tan(37^\circ) $$ 6. **Evaluate $\tan(37^\circ)$:** $\tan(37^\circ) \approx 0.7536$ 7. **Final calculation:** $$ RQ = 9.8 \times 0.7536 = 7.38528 $$ 8. **Answer:** The length of the flagpole RQ is approximately **7.39 m**.