Chapter 8.3, Problem 66PS

Solution

To explain : A worker who is $6$ feet $2$ inches tall walk down the center of the walkway without ducking.

The worker can walk down the center of the walkway without ducking as his height is less than $6.6\text{ feet}$ .

Given information :

A circular utility tunnel $8$ feet in diameter has a $6$ foot wide walkway across its bottom.

Formula used:

Pythagoras Theorem:

  ${\left(\text{Hypotenuse}\right)}^2={\left(\text{Perpendicular}\right)}^2+{\left(\text{Base}\right)}^2$

Explanation :

Draw the figure.

  

Use Pythagoras Theorem to find $OA$ .

  $\begin{array}{c}{\left(OB\right)}^2={\left(OA\right)}^2+{\left(AB\right)}^2\\ 16={\left(OA\right)}^2+9\\ {\left(OA\right)}^2=7\\ OA=2.6\end{array}$

The length of $AC$ will be,

  $\begin{array}{c}AC=OC+OA\\ =4+2.6\\ =6.6\text{ feet}\end{array}$

Therefore, the worker can walk down the center of the walkway without ducking as his height is less than $6.6\text{ feet}$ .