Chapter 9.1, Problem 49E

(a)

To determine

To find: The distance between plane and first town.

Answer to Problem 49E

The distance between plane and first town is $\text{59155}$ ft.

Explanation of Solution

Given information: passenger sees two towns to the left of plane.

Given figure:

  

Calculation:

The two towns are viewed from the left of the airplane.

The objective is to find the distance $d$ from the airplane to first plane.

Reconstruct the figure as shows below:

  

From the figure, the trigonomentric indentity for $\sin {25}^0$ is:

  $\begin{array}{c}\sin {25}^0=\frac{\text{Opposite side}}{\text{Hypotenuse}}\\ =\frac{25000}{d}\end{array}$

Solve for $d.$

  $\begin{array}{c}d=\frac{25000}{\sin {25}^0}\\ =\frac{25000}{0.422618}\\ =59755.07\end{array}$

Therefore. The distance $d$ from the airplane to the first town is 59155 ft.

(b)

To determine

To find: The horizontal distance $x$ between airplane and first town.

Answer to Problem 49E

The horizontal distance $x$ between airplane and first town is$\text{53613}$ .

Explanation of Solution

Given information: passenger sees two towns to the left of plane.

Given figure:

  

Calculation:

The objective is to find the horizontal distance $x$ from the airplane to the first town.

From the figure, the trigonometric identity for $\cos {25}^0$ is:

  $\begin{array}{c}\cos {25}^0=\frac{\text{Adjacent side}}{\text{Hypotenuse}}\\ =\frac{x}{59155}\end{array}$

Solve for $x$ .

  $\begin{array}{c}x=59155*\cos {25}^0\\ =59155*0.9063077870\\ =53612.63\end{array}$

Therefore, The horizontal distance $x$ from the plane to the first town is 53613.

(c)

To determine

To find: Distance $y$ between two towns, and explain process.

Answer to Problem 49E

Distance $y$ between two towns is $39688$ft.

Explanation of Solution

Given information: passenger sees two towns to the left of plane.

Given figure:

  

Calculation:

The objective is to find the distance $y$ between two towns.

Reconstruct the figure as shown below:

  

From the figure, the trigonometric identity for $\tan {15}^0$ is:

  $\begin{array}{c}\tan {15}^0=\frac{\text{Opposite side}}{\text{Adjacent side}}\\ =\frac{25000}{x+y}\end{array}$

Substitute the value of $x$ and solve for $y$ .

  $\begin{array}{c}\tan {15}^0=\frac{25000}{53613+y}\\ 53613+y=\frac{25000}{\tan {15}^0}\\ 53613+y=\frac{25000}{0.2679491924}\\ 53613+y=93301.27020\\ y=93301.27020-53613\\ y=39688.27020\end{array}$

Therefore, the distance $y$ between two towns is 39688 ft.