A highway engineer specifies that a certain section of the roadway covering a horizontal distance of 2 km should have an upgrade of 8%. Compute the change in elevation of this section of the road.

Question

anonymous · Answer

|dw:1373600846343:dw|
$$\frac{\theta}{90^\textrm{o}}=8\% \
\:\
\theta = 8\%\cdot90^\textrm{o}=7.2^\textrm{o} \
\tan\theta = \frac{\textrm{opp}}{\textrm{adj}}=\frac{\textrm{opp}}{2~\textrm{km}} \
\:\
\begin{align}
  \textrm{opp}&=2~\textrm{km}\cdot\tan\theta = 2~\textrm{km}\cdot\tan7.2^\textrm{o} \
  &\approx0.252659~\textrm{km}=252.659~\textrm{m}
\end{align}$$