A road sign at the top of a mountain indicates that for the next 4 miles the grade is 12%. Find the angle of the grade and the change in elevation for a car descending the mountain.

Answer 1

The grade of an incline is its vertical rise in some units per every 100 horizontal run in the same units.
so
rise/run = tan slope = .12
so slope = tan^-1 .12 = 6.8 degrees
height in miles = .12 run in miles
( the question is ambiguous. I am assuming the 4 miles is on the map, horizontal, rather than on the odometer , hypotenuse)
height change = .12*4 miles = .48 miles down
or .48*5280 = 2534 feet down

Answer 2

A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9.5° (see figure). Find the change in elevation for a car descending the 4-mile stretch. (Round your answer to two decimal places.)