SOLUTION: The westbound U.S. Highway 74 truck route through North Carolina near the Tuckaseegee River has a downhill grade of 5%.� (a) Explain what a 5% downhill grade means. A 5% downhi

Question 1038639: The westbound U.S. Highway 74 truck route through North Carolina near the Tuckaseegee River has a downhill grade of 5%.�
(a) Explain what a 5% downhill grade means.
A 5% downhill grade for a segment of road means that the decrease in elevation of the road over the segment is 5% of the change in horizontal distance over the same segment. In other words, for every______?_____ horizontal feet, the road descends 5 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.)

____________�
(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 5% downhill grade?

______?______feet
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The percent of grade is the rise or fall per 100 horizontal units. In other words, a 5% grade would mean the road rises or falls 5 in (or feet or miles) for every 100 in (or feet or miles) horizontally travelled.
One question per post please.
John

My calculator said it, I believe it, that settles it

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