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, we can use the concept of trigonometry, specifically the tangent function. Given: - Height of the lookout tower = 75 feet - Angle of depression = \(28^{\circ}\) We can use the tangent function to find the horizontal distance. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Let's denote the horizontal distance as \(x\). Using the tangent function, we have: \[ \tan(28^{\circ}) = \frac{75}{x} \] To find the horizontal distance \(x\), we can rearrange the equation to solve for \(x\): \[ x = \frac{75}{\tan(28^{\circ})} \] Now, we can calculate the value of \(x\) using a calculator. The horizontal distance between Zack and the water fountain is approximately 266.5 feet.