T8anannicarmendge T8anannicarmendge

13-10-2016
Mathematics

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A road has a 10% grade. 1. What is the angle of elevation of the road? 2. If the road is 2km long, how much does it rise?

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HomertheGenius HomertheGenius

17-10-2016

1. m = rise/run
m = 10/100 = 0.1
tan α = 0.1
α = tan^(-1) 0.1
α = 5.71 °
2. 2 km = 2,000 m
x² + ( 0.1 x )² = 2,000²
x² + 0.01 x² = 4,000,000
1.01 x² = 4,000,000
x = 1,990 m
h = 1,990 m * 0.1
h = 199 m
The road rises 199 m.

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