Chapter 4.8, Problem 40E

To determine

To identify: The angle when the pilot wants to fly directly to the airport.

Answer to Problem 40E

The angle of bearing would be ${207.98}^{\circ }$ .

Explanation of Solution

Given Information:

An airplane is 160 miles north and 85 miles east of an airport.

Concept Involved:

Use the trigonometric formula such that

  $\tan \theta =\frac{\text{Perpendicular}}{\text{Base}}$

Consider the angle between plane and airport be x .

  

From the above,

  $\begin{array}{l}\tan x=\frac{160}{85}\\ \Rightarrow x={\tan }^{-1}\left(\frac{160}{85}\right)\\ x={\tan }^{-1}\left(1.88235294118\right)\\ x={62.02}^{\circ }\end{array}$

Since the plane is flying due east, it has to turn ${90}^{\circ }$ to face south.

Then,

  ${90}^{\circ }-{62.02}^{\circ }={27.98}^{\circ }$

Before it turns the extra ${27.98}^{\circ }$ to fly towards the airport.

  ${90}^{\circ }+{27.98}^{\circ }={117.98}^{\circ }$

The plane turns through the exterior angle of the triangle.

That is

  ${90}^{\circ }+{117.98}^{\circ }={207.98}^{\circ }$

Conclusion:

The angle of bearing would be ${207.98}^{\circ }$ .