Question

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

Answer 1

Answer:

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

Part b) The rise is $0.2\ km$

Step-by-step 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

$1/10=y/2$

$y=2/10=0.2\ km$