SOLUTION: I need help on how to solve this trig question. Any help would be great. Thank you A certain westbound U.S. highway truck route near a river has a downhill grade of 2%. (a) Exp

Question 1052943: I need help on how to solve this trig question. Any help would be great. Thank you
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.
Find the angle of descent for the road using the tangent function. (Round your answer to two decimal places.) (Has to be in degrees)

(b) Explain how you could have used the cotangent function to have found the answer to part (a).
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?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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.
------
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
================
(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

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