Answer:
159 km
Explanation:
In order to find the distance from starting point to ending point, we have to find the net displacement.
To do that, we have to resolve each displacement along the x- and y- direction.
Here the displacements are:
1) 84 km on a bearing of 17°
2) 135 km on a bearing of 107°
Keeping in mind that the bearing is measured as clockwise from north, we resolve each displacement as follows:
1)
[tex]A_x = (84)(sin 17^{\circ})=24.6 km\\A_y=(84)(cos 17^{\circ})=80.3 km[/tex]
2)
[tex]B_x=(135)(sin 107^{\circ})=129.1 km\\B_y=(135)(cos 107^{\circ})=-39.5 km[/tex]
Therefore, the components of the net displacement are
[tex]R_x=A_x+B_x=24.6+129.1=153.7 km\\R_y=A_y+B_y=80.3-39.5=40.8 km[/tex]
So, the distance from starting to ending point is the magnitude of the net displacement:
[tex]d=\sqrt{R_x^2+R_y^2}=\sqrt{153.7^2+(-40.8)^2}=159.0 km[/tex]
