Chapter 4, Problem 41RE

To determine

Find the vertical rise if the train in that distance.

Answer to Problem 41RE

The vertical rise is 0.073 kilometers

Explanation of Solution

Given:

A train travels at 3.5 kilometres on a straight track with a grade of ${1.2}^{\circ }$

This situation forms a right angled triangle and let it be right angled triangle $ABC$ where

AC is the distance 3.5 kilometers and the angle C is ${1.2}^{\circ }$

AB is the vertical rise.

  

By using trigonometry

  $\begin{array}{l}\frac{AB}{AC}=\sin {1.2}^{\circ }\\ AB=AC\times \sin {1.2}^{\circ }\\ =3.5\times 0.0209=0.073\end{array}$

So, the vertical rise is 0.073 kilometers