3. \( 28 c k \) is standing at the top of a lookout tower and spots a water fountain below. If the lookout tower Is 75 feet tall and the angle of depression is \( 28^{\circ} \), what is the horizontal distance between Zack and the water fountain?

To find the horizontal distance between Zack and the water fountain, you can use trigonometry. Since the angle of depression is \(28^{\circ}\), the corresponding angle of elevation from the fountain to Zack is also \(28^{\circ}\). We'll use the tangent function, which relates the opposite side (the height of the tower) to the adjacent side (the horizontal distance we want to find): \[ \tan(28^{\circ}) = \frac{\text{height}}{\text{horizontal distance}} = \frac{75 \text{ feet}}{d} \] Rearranging gives: \[ d = \frac{75 \text{ feet}}{\tan(28^{\circ})} \] Calculating \( \tan(28^{\circ}) \) (approximately \(0.5317\)) yields: \[ d \approx \frac{75}{0.5317} \approx 141.77 \text{ feet} \] So, the horizontal distance between Zack and the water fountain is approximately \(141.77\) feet.