Chapter 12, Problem 36CR

To determine

To find: The distance travelled by the Dog from the initial point to the final point.

Answer to Problem 36CR

The distance between initial point and final point is 16.2 mile.

Explanation of Solution

Given Information:

Dog travels in three directions covering the same distance every time

Formula used:

Using trigonometry in right triangle, we have

  $\cos {45}^{\text{o}}=\frac{\text{Adjacent}\text{side}}{\text{Hypotenuse}}$

Calculation:

Let $A$ be the initial point and $D$ be the final point

Dog travels from $A\text{to}B,$ then $B\text{to}C$ and finally from $C\text{to}D.$

Draw perpendicular from $C$ to produced $AB$ meeting it at point $O.$

  

Now, in $\Delta BOC,\angle BOC={90}^{\text{o}}\text{and}\angle OBC={45}^{\text{o}}$

Using trigonometry, we have

  $\begin{array}{l}\cos {45}^{\text{o}}=\frac{\text{Adjacent}\text{side}}{\text{Hypotenuse}}\\ \therefore \cos {45}^{\text{o}}=\frac{BO}{BC}\\ \therefore \frac{1}{\sqrt{2}}=\frac{BO}{6}\\ \therefore BO=3\sqrt{2}\end{array}$

We know that distance travelled along diagonal will be greater than the distance travelled straight.

So, $BO<BC$

Also, $CD=OE$ … (opposite sides of rectangle)

  $\therefore AD=AB+BO+OE=16+3\sqrt{2}=16.2$

Hence, the distance between initial point and final point is 16.2 mile.