a) suppose u walk 18m straight west and then 25m straight south. how far are u from your starting point, and what is the compass direction of a line connecting your starting pointto your final position?
b) repeat again, but now you first walk 25m north and then 18m east. is that consistent with your result in (a)?
angle: arctan 25/18 S of W.
arctan 25/18=54 deg S of W.
how far: sqrt(25^2+18^2)=....
a) To determine the distance and compass direction of the line connecting your starting point to your final position, we can use the Pythagorean theorem and trigonometry.
First, let's calculate the distance from the starting point to the final position using the Pythagorean theorem:
Distance = √((distance west)^2 + (distance south)^2)
Distance = √((18m)^2 + (25m)^2)
Distance = √(324m^2 + 625m^2)
Distance = √(949m^2)
Distance ≈ 30.81m
Next, let's determine the compass direction of the line connecting your starting point to your final position. We can use trigonometry to find the angle.
Angle = arctan((distance south) / (distance west))
Angle = arctan(25m / 18m)
Angle ≈ 54.74°
Therefore, you are approximately 30.81m away from your starting point, and the compass direction of the line connecting your starting point to your final position is approximately 54.74° south of west.
b) If you first walk 25m north and then 18m east, we need to calculate the new distance and compass direction.
Distance = √((distance east)^2 + (distance north)^2)
Distance = √((18m)^2 + (25m)^2)
Distance = √(324m^2 + 625m^2)
Distance = √(949m^2)
Distance ≈ 30.81m
Angle = arctan((distance north) / (distance east))
Angle = arctan(25m / 18m)
Angle ≈ 54.74°
The new distance and compass direction are the same as in part (a). Therefore, it is consistent with the result in (a).
So, regardless of the order you walk, the distance will always be approximately 30.81m, and the compass direction of the line connecting the starting point to the final position will always be approximately 54.74° south of west.