Answer:
B) 71.5 [km]
Explanation:
To solve this problem we will decompose each of the directions in the x & y axes.
To solve this problem we will decompose each of the directions in the x & y axes. also for a greater understanding of the angles, you should look at the attached image, which contains the orientations for each angle (clockwise or counterclockwise).
59.0 km in a direction 30.0° east of north
[tex]d_{1x}= 59*sin(30) = 29.5[km]\\d_{1y}= 59*cos(30) = 51.09[km][/tex]
58.0 km due south
[tex]d_{2y} = - 58 [km]\\[/tex]
It flies 100 km 30.0° north of west
[tex]d_{3x}= - 100*cos(30) = -86.6[km]\\d_{3y} = 100*sin(30)= 50 [km][/tex]
Now we sum algebraically the components
[tex]d_{x}=29.5-86.6 = -57.1[km]\\d_{y}=51.09 -58+50=43.09[km]\\\\[/tex]
Using the Pythagorean theorem we can find the magnitude of the displacement.
[tex]d = \sqrt{(57.1)^{2} +(43.09)^{2} } \\d= 71.53[km][/tex]
