Question 1052943
A certain westbound U.S. highway truck route near a river has a downhill grade of 2%.
(a) Explain what a 2% downhill grade means.


A 2% downhill grade for a segment of road means that the decrease in elevation of the road over the segment is 2% of the change in horizontal distance over the same segment. In other words, for every___?___horizontal feet, the road descends 2 feet, so the road has a slope of___?___ vertical feet per horizontal foot.
2% --> 2 ft vertical for 100 feet horizontal.
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Find the angle of descent for the road using the tangent function. (Round your answer to two decimal places.) (Has to be in degrees)
Tan(angle) = 0.02
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(b) Explain how you could have used the cotangent function to have found the answer to part (a).
cot = 1/tan
There's no reason to use the cot.  Few, if any, calculators have a COT button.

The cotangent function would relate the horizontal change to the vertical change of the road, so we could have used the equation 
cot(θ) =  
 
instead of
tan(θ) =  
 

(c) What is the elevation change over 2.5 miles on a road with a 2% downhill grade?
For 2.5 miles horizontal:
2.5*0.02 = 0.05 miles