Posted by **Henry** on Thursday, February 5, 2009 at 11:24pm.

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.

- Pre-Calculus -
**Damon**, Friday, February 6, 2009 at 10:42am
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

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