If a car is climbing a hill at a \( 10^{\circ} \) angle, how many vertical feet will the car travel every 500 feet of road? Give your answer rounded to the nearest foot. \( \left(\right. \) Note: \( \sin \left(10^{\circ}\right) \approx 0.174, \cos \left(10^{\circ}\right) \approx 0.985 \), \( \left.\tan \left(10^{\circ}\right) \approx 0.176\right) \) 88 88 493

To find the vertical distance the car travels while climbing a hill at a \(10^{\circ}\) angle over 500 feet of road, you can use the sine function. The formula for vertical distance is given by: \[ \text{Vertical distance} = \text{Length of the road} \times \sin(\text{angle}) \] Plugging in the numbers: \[ \text{Vertical distance} = 500 \text{ feet} \times \sin(10^{\circ}) \approx 500 \times 0.174 \approx 87 \text{ feet} \] Rounded to the nearest foot, the car will travel approximately 87 feet vertically. When cruising up that scenic hill, think about how much energy the engine is using to overcome gravity! The steeper the angle, or the longer the distance, the more power is required. It’s like going up a giant roller coaster—more height means more thrill, but also more work for your vehicle. Understanding these factors can help in managing fuel consumption and vehicle maintenance on hilly terrains.