1. **Problem statement:** Tarzan wants to find the width of the river, which corresponds to the vertical distance from point A to point B. 2. **Setup:** We have a right triangle formed by points A, B, and C. Tarzan walks 28 paces from A to C along the riverbank, then 10 paces further to point D, then turns perpendicular to the river and walks 14 paces to point E, where C lines up with A vertically. 3. **Known distances:** - AC = 28 paces - CD = 10 paces - DE = 14 paces 4. **Goal:** Find the width of the river, which is the length AB. 5. **Analysis:** Since DE is perpendicular to the river, triangle CDE is a right triangle with legs CD = 10 and DE = 14. 6. **Calculate CE using Pythagoras:** $$ CE = \sqrt{CD^2 + DE^2} = \sqrt{10^2 + 14^2} = \sqrt{100 + 196} = \sqrt{296} $$ 7. **Calculate CE:** $$ CE = \sqrt{296} \approx 17.2 \text{ paces} $$ 8. **Since point E lines up vertically with A, the horizontal distance from A to C plus CD equals AC + CD = 28 + 10 = 38 paces. The horizontal distance from A to E is 38 paces, and the vertical distance from A to B is the same as from E to B (since E is vertically aligned with A). The width of the river AB equals DE = 14 paces. But we need to confirm this by considering the right triangle formed by A, B, and E. 9. **Triangle ABE is right angled with AE = 38 paces (horizontal) and BE = AB (vertical, the river width). Since C lines up with A vertically after walking DE, the width AB equals DE = 14 paces. 10. **Final answer:** The width of the river is $$ \boxed{14} \text{ paces} $$