Chapter 8, Problem 56RE

(a)

To determine

To find:The distance of the sailboat from the island.

Explanation of Solution

The distance is calculated as,

  $\begin{array}{c}D=t\times v\\ =\left(18\text{mi}/\text{h}\right)\left(4\text{h}\right)\\ =72\text{mi}\end{array}$

Therefore, the distance of the sailboat from the island is $72\text{mi}$ .

(b)

To determine

To find: The angle of turn of the boat.

Explanation of Solution

Consider the figure shown below.

  

Apply the law of cosine in triangle ABC.

  $\begin{array}{c}b=\sqrt{a^2+c^2-2ac\cos B}\\ =\sqrt{{72}^2+{200}^2-2\left(72\right)\left(200\right)\cos 15°}\\ b=131.77\end{array}$

Now, apply the law of cosine.

  $\begin{array}{c}\frac{\sin B}{b}=\frac{\sin C}{c}\\ \sin C=\frac{200}{131.77}\sin 15°\\ C=23.13°+90°\\ =113.13°\end{array}$

The required angle of turn of boat is calculated as,

  $\begin{array}{c}\theta =180°-133.13°\\ =66.87°\end{array}$

Therefore, the required angle of turn is $66.87°$ .

(c)

To determine

To find: The amount of time added to the trip.

Explanation of Solution

The total distance covered is,

  $\begin{array}{c}TD=BC+CA\\ =72+131.77\\ =203.77\end{array}$

The extra distance covered,

  $\begin{array}{c}ED=203.77-200\\ =3.77\text{mi}\end{array}$

Thus, the extra time added,

  $\begin{array}{c}Extratime=\frac{3.77}{18}\\ =0.21\text{hr}\\ =\text{12}\text{.5}\text{min}\end{array}$

Therefore, the extra time added is $12.5\text{min}$ .