West of a city, a certain eastbound route is straight and makes a steep descent toward the city. The highway has a 14% grade, which means that its slope is - 14 100. Driving on this road, you notice from elevation signs that you have descended a distance of 1000 ft. What is the change in your horizontal distance in miles

1.35 miles

Explanation:

Since the slope is 14% grade = - 14/100. This is a negative slope.

The distance of 1000 ft descended is a vertical descent, so assuming our initial position is 0, and Δx is the change in horizontal distance.

tanθ = - 14/100 = (0 - 1000) / Δx = - 1000) / Δx

-14/100 = - 1000) / Δx

Δx = - 1000 * - 100/14 = 7142.86 ft

5280 ft = 1 mile

7142.86 ft = 7142.86/5280 miles = 1.353 miles ≅ 1.35 miles