1. **State the problem:** A surfer is riding a 7-foot wave, and the angle of depression from the surfer to the shoreline is 10°. We need to find the distance from the surfer to the shoreline. 2. **Identify the right triangle and trigonometric function:** The wave height (7 feet) is the vertical leg opposite the angle of depression (10°). The distance to the shoreline is the adjacent side to the angle. 3. **Use the tangent function:** Tangent relates opposite and adjacent sides in a right triangle: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 10^\circ$, opposite = 7 feet, adjacent = distance $d$. 4. **Set up the equation:** $$\tan(10^\circ) = \frac{7}{d}$$ 5. **Solve for $d$:** $$d = \frac{7}{\tan(10^\circ)}$$ 6. **Calculate $\tan(10^\circ)$:** $\tan(10^\circ) \approx 0.1763$ 7. **Evaluate $d$:** $$d = \frac{7}{0.1763} \approx 39.7$$ 8. **Interpretation:** The distance from the surfer to the shoreline is approximately 39.7 feet. **Note:** The problem's diagram and given answer 72.0 might correspond to a different angle or setup, but based on the given angle of depression 10° and wave height 7 feet, this is the correct calculation. "slug": "surfer distance","subject": "trigonometry","desmos": {"latex": "y=7/\tan(10^\circ)","features": {"intercepts": true,"extrema": true}},"q_count": 2