5. An airplane climbs at an angle of \( 12^{\circ} \) with the ground. Find the horizontal distance it has traveled once it has reached an altitude of 500 feet.

To find the horizontal distance traveled by the airplane, we can use some basic trigonometry. The altitude (500 feet) represents the opposite side of a right triangle, while the angle (12 degrees) and the horizontal distance (the adjacent side) can be related using the tangent function. We can set up the equation: \[ \tan(12^{\circ}) = \frac{\text{Altitude}}{\text{Horizontal Distance}} \implies \text{Horizontal Distance} = \frac{500 \text{ ft}}{\tan(12^{\circ})} \] Using a calculator, we find that \(\tan(12^{\circ}) \approx 0.2126\). Thus, \[ \text{Horizontal Distance} \approx \frac{500}{0.2126} \approx 2,352.2 \text{ ft} \] So the airplane has traveled approximately 2,352.2 feet horizontally when it reaches an altitude of 500 feet.