Chapter 8.2, Problem 50AYU

(a)

To determine

To find: Thedistance of the ship from the light house from the point $P$ .

Answer to Problem 50AYU

The distance of the ship from the light house is $3.21\text{mile}$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Figure 1

The distance between the two light house is $3$ miles.

The angle between the line of sight from the ship directly to the shore is $15°$ and $30°$ .

Calculation:

Consider the diagram is shown in Figure 2

Figure 1

Consider the value of angle $P$ is,

  $\begin{array}{c}P=180°-\left(90°+15°\right)\\ =75°\end{array}$

Consider the measure of angle $R$ is,

  $\begin{array}{c}R=15°+35°\\ =50°\end{array}$

Consider the measure of angle $Q$ is,

  $\begin{array}{c}Q=180°-\left(75°+55°\right)\\ =55°\end{array}$

Consider the law of sine is,

  $\frac{\sin Q}{q}=\frac{\sin R}{r}$

Then,

  $\begin{array}{l}\frac{\sin 55°}{q}=\frac{\sin 30°}{3\text{mile}}\\ q=3.21\text{mile}\end{array}$

(b)

To determine

To find: The distance of the ship from the light house from the point $Q$ .

Answer to Problem 50AYU

The distance of the ship from the light house is $3.78\text{mile}$ .

Explanation of Solution

Calculation:

Consider the law of sine is,

  $\frac{\sin O}{p}=\frac{\sin R}{r}$

Then,

  $\begin{array}{l}\frac{\sin 75°}{p}=\frac{\sin 50°}{3\text{mile}}\\ p=3.78\text{mile}\end{array}$

(c)

To determine

To find: The distance of the ship from the shore.

Answer to Problem 50AYU

The distance of the ship from shore is $3.1\text{mile}$ .

Explanation of Solution

Consider the distance of the ship from the shore is,

  $\begin{array}{c}h=3.21\sin 75°\\ =3.1\text{mile}\end{array}$