Question

If a car is climbing a hill at a 15° angle, how many horizontal feet will the car travel every 1,000 feet of road if the car gains 259 feet of vertical feet? Round your answer to the nearest foot.

Answer 1

For every 1,000 feet of road, the car will travel approximately 245.5 feet horizontally.

Step-by-step explanation:

To determine how many horizontal feet a car will travel for every 1,000 feet of road when climbing a hill at a 15° angle, we need to calculate the horizontal displacement. The horizontal displacement can be found using the trigonometric function cosine.

Given that the car gains 259 feet of vertical height, we can use the formula: horizontal displacement = vertical displacement / cosine(angle).

Using the values, horizontal displacement = 259 / cos(15°).

Calculating the value gives us a horizontal displacement of approximately 245.5 feet. Therefore, for every 1,000 feet of road, the car will travel approximately 245.5 feet horizontally.