1. **Problem statement:** You are standing at the edge of the Grand Canyon, 1.5 m above the cliff edge. The canyon is 498 m wide horizontally, and the angle of depression to the bottom is 75°. We need to find the depth of the canyon from the cliff edge to the bottom, rounded to the nearest meter. 2. **Understanding the problem:** The angle of depression of 75° means the line of sight from your eyes to the bottom of the canyon makes a 75° angle below the horizontal. 3. **Set up the right triangle:** - The horizontal distance across the canyon is the adjacent side: $498$ m. - The vertical depth from the cliff edge to the bottom is the opposite side, which we want to find. - The angle between the horizontal and the line of sight is $75^\circ$. 4. **Use trigonometric ratios:** The tangent of the angle relates opposite and adjacent sides: $$\tan(75^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\text{depth}}{498}$$ 5. **Solve for depth:** $$\text{depth} = 498 \times \tan(75^\circ)$$ 6. **Calculate $\tan(75^\circ)$:** Using a calculator, $\tan(75^\circ) \approx 3.732$ 7. **Calculate depth:** $$\text{depth} = 498 \times 3.732 = 1858.536$$ 8. **Adjust for eye height:** Since your eyes are 1.5 m above the cliff edge, the total depth from your eye level to the bottom is $1858.536$ m, so the depth from the cliff edge is: $$\text{depth from cliff edge} = 1858.536 - 1.5 = 1857.036$$ 9. **Round to nearest meter:** $$\boxed{1857 \text{ meters}}$$ This is the depth of the Grand Canyon at this point from the cliff edge to the bottom.