Chapter 8.7, Problem 10WE

(a)

To determine

To Find : The angle of elevation of the road.

Answer to Problem 10WE

The angle of elevation of the road is $5.7°$ .

Explanation of Solution

Given information:

A road has $10\%$ grade.

Suppose the angle of elevation of the road is x then,

  $\begin{array}{l}\tan x=0.1\hfill \\ \tan x=\tan 5.7°\hfill \\ x=5.7°\hfill \end{array}$

Hence, the angle of elevation of the road is $5.7°$ .

(b)

To determine

To Find : The height of the road by which it is risen.

Answer to Problem 10WE

The road will rise at the height of 200m.

Explanation of Solution

Given information:

If the road is 2 km long.

Let the road will rise at the height of h,

Apply the tan formula in the right angle triangle,

  $\begin{array}{l}\tan x=\frac{\text{Perpendicular}}{\text{Base}}\hfill \\ 0.1=\frac{h}{2}\hfill \\ h=0.2km\hfill \\ h=0.2\times 1000\hfill \\ h=200m\hfill \end{array}$

Hence, the road will rise at the height of 200 m.