First a diagram of the situation is made.
The components are obtained for each displacement.
# Displacement 1
Horizontal axis component
cos(370)=D1D1xD1x=D1cos(370)D1x=500m∗cos(370)D1x=399m
Vertical axis component
sin(370)=D1D1yD1y=D1sin(370)D1y=500m∗sin(370)D1y=301m
Expressing as a vector
D1=(399i+301j)[m]
# Displacement 2
Horizontal axis component
sin(600)=D2D2xD2x=D2sin(600)D2x=1000m∗sin(600)D2x=866m
Vertical axis component
cos(600)=D2D2yD2y=D2cos(600)D2y=1000m∗cos(600)D2y=500m
Expressing as a vector
D2=(−866i+500j)[m]
The total displacement is
DR=D1+D2DR=(399i+301j)[m]+(−866i+500j)[m]DR=[(399−866)i+(301+500)j][m]DR=(−467i+801)[m]
The run module is calculated using the Pythagorean theorem.
∣DR∣=(−467)2+(801)2∣DR∣=927m
the module of the run is ∣DR∣=927m
The direction with respect to the + i axis is
tanθ=(−467801)θ=tan−1(−467801)θ=−59.750+1800=1200 Measured from the East direction (+ i)
Note: Being a negative component, the resulting angle will be reflected as in quadranta IV, but 180 degrees must be added to reflect it in quadrant II
with respect to the north the angle is 1200−900=300
Expressing the closest coordinate axis.
30°west by north
the the orientation of the run is 30°west by north
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