Final answer:
To determine the change in elevation over a 4-mile road stretch with a 9.5-degree grade, we first convert the road length to feet and then use the sine function to relate the road's grade to the elevation change. The calculation reveals that the change in elevation is approximately 3463.68 feet when rounded to two decimal places.
Step-by-step explanation:
To find the change in elevation for a car descending a 4-mile stretch with a grade of 9.5°, we first need to convert miles to a more useful unit for trigonometric calculations. There are 5280 feet in a mile, so 4 miles is equivalent to 21120 feet. Given that the road descends at a 9.5° angle, we can use the sine function to determine the change in elevation because sine relates the opposite side of a right-angled triangle (the change in elevation, in this case) to the hypotenuse (the length of the road).
The change in elevation (E) can be calculated using the formula E = sin(angle) × hypotenuse. Substituting the known values, we have E = sin(9.5°) × 21120 feet.
Using a calculator set to degrees, we find that sin(9.5°) is approximately 0.164. Therefore, the change in elevation is E = 0.164 × 21120 feet = 3463.68 feet. Rounding to two decimal places gives us a change in elevation of 3463.68 feet.