Question

A road has a 10% grade, meaning increasing 1 unit of rise to every 10 units of run.

a) What is the elevation of the road to the nearest degree?
b) If the road is two km long, how much does it rise? Round your answer to the nearest tenth?

Answer 1

Part a) The elevation of the road is
`6\°`

Part b) The rise is
`0.2\ km`

Explanation:

Part a) What is the elevation of the road to the nearest degree?

Let

y-----> the rise of the road ( vertical distance)

x ----> the run of the road (horizontal distance)

we have

y/x=1/10

we know that

The ratio y/x is equal to the tangent of the angle of the elevation of the road

Let

`\theta` ----> angle of the elevation of the road

`tan(\theta)=y/x`

`tan(\theta)=1/10`

`\theta=arctan(1/10)=6\°`

Part b) If the road is two km long, how much does it rise?

using proportion

`1/10=y/2`

`y=2/10=0.2\ km`