Chapter 9.8, Problem 26E

a.

To determine

To find the height of $x$ above the boat.

Answer to Problem 26E

The height of $x$ above the boat $x=300ft$

Explanation of Solution

Given:

  

Calculation:

  $\begin{array}{l}\text{In }\Delta ABC,\\ \sin 30=\frac{\overline{AB}}{BC}\Rightarrow \overline{AB}=x=600\ast \sin 30\\ \Rightarrow \overline{AB}=x=600\ast 0.5=300ft\end{array}$

Thus, the height of $x$ above the boat $x=300ft$

b.

To determine

To find the height above the boat decreases if the tow line makes with the horizontal decreases by $3^0$.

Answer to Problem 26E

The height above the boat decreases = $300-272=28ft$

Explanation of Solution

Given:

The angle that the tow line makes with the horizontal decreases by $3^0$ .

Calculation:

  $\begin{array}{l}\text{In }\Delta ABC,\\ $ \sin {(30-3)}^0=\frac{\overline{AB}}{BC}\Rightarrow \overline{AB}=x=600\ast \sin {27}^0$\Rightarrow \overline{AB}=x=600\ast 0.454=272.39\approx 272ft\end{array}$

Hence, the height above the boat decreases = $300-272=28ft$