Chapter 4, Problem 42RE

To determine

Distance between the base of the pole and point to which wire is attached to ground.

Answer to Problem 42RE

Distance between the base of the pole and point to which wire is attached to ground is

  $x=40.61\text{ft}$

Explanation of Solution

Given:

Height of telephone pole = $25\text{ft}$

Angle of elevation is ${\text{52}}^0$

Pole is perpendicular to ground

As the pole is placed vertically so a triangle is formed by pole, cable and ground.

Distance between the base of the pole and the point which the wire is attached to the ground is a right angled triangle with opposite side of the angle ${\text{52}}^0$ .

Let distance is $x$ .

Now, using cosine function adjacent side will be

  $\begin{array}{l}\cos \left({\text{52}}^0\right)=\frac{\text{Opposite side}}{\text{Adjacent side}}\\ =\frac{\text{pole length}}{\text{ground point of wire and pole base distance}}\\ =\frac{25}{x}\end{array}$

  $\begin{array}{l}\Rightarrow x=\frac{25}{\cos \left({\text{52}}^0\right)}\\ =\frac{25}{0.6157}\\ \Rightarrow x=40.61\text{ft}\end{array}$