The Aster's final position from her initial position is determined as 45.3 m.
The direction that she has to head to return to her initial position is 30° west of north.
The distance traveled by the person can be determined by making a sketch of the person's journey.
From the initial distance traveled and the second distance distance the angle between the two position is calculated as;
θ = 37⁰ + 20⁰ = 57⁰
The distance opposite to the angle is resultant displacement and it is calculated as follows;
r² = (70²) + (82²) - (2 x 70 x 82) x cos(57)
r² = 5,371.54
r = √5,371.54
r = 73.3 m
Haven walked 28 m in the same direction to her initial position, the remaining distance is calculated as follows;
d = 73. 3 m - 28 m
d = 45.3 m
Thus, the Aster's final position from her initial position is determined as 45.3 m.
The direction that she has to head to return to her initial position is 30° west of north.
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Answer:
See below
Explanation:
I will break the legs into vertical and horizontal components then add them
Horizontal = 70 cos 37 + 82 cos 340 + 28 cos 120 = 118.96 m
Vertical = 70 sin 37 + 82 sin 340 + 28 sin 120 = 38.33 m
Resultant distance from origin is found via pythag theorem
d^2 = 118.96^2 + 38.33^2 d = 124.98 m
direction FROM origin is arctan ( 38.33/118.96) = 17.86°
to get BACK to the origin , will have to walk 180 degrees from this = 197.86°
