Explanation:
We can use trigonometry to solve this problem. The grade of the road is given as an angle of 9.5°. This means that for every 1 unit of horizontal distance traveled, the elevation changes by the tangent of 9.5°.
We want to find the change in elevation for a car descending the 4-mile stretch. To do this, we can multiply the length of the road by the tangent of the grade angle:
Change in elevation = 4 miles x tan(9.5°)
Using a calculator, we can find that tan(9.5°) = 0.1664. Substituting this value into the equation, we get:
Change in elevation = 4 miles x 0.1664 ≈ 0.67 milesTo convert this to feet, we can multiply by the number of feet in a mile:
Change in elevation = 0.67 miles x 5,280 feet/mile ≈ 3,539 feetTherefore, the change in elevation for a car descending the 4-mile stretch is approximately 3,539 feet.