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)?
see other post.
a) To find the distance from your starting point, you can use the Pythagorean theorem as you have moved in two perpendicular directions (west and south). The Pythagorean theorem states that the square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b). In this case, the sides are 18m and 25m.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 18^2 + 25^2
c^2 = 324 + 625
c^2 = 949
c ≈ √949
c ≈ 30.8m
So, you are approximately 30.8 meters away from your starting point.
To find the compass direction of the line connecting your starting point to your final position, you can use trigonometry. The tangent function relates the angles and sides of a right triangle. In this case, you can use the tangent to find the angle of the line connecting your starting point to your final position.
Using the tangent function:
tan(θ) = opposite/adjacent
tan(θ) = 18/25
θ ≈ 37.8 degrees
Therefore, the compass direction of the line connecting your starting point to your final position is approximately 37.8 degrees south of west.
b) If you first walk 25m north and then 18m east, you can use the same approach as above to find the distance and direction.
Using the Pythagorean theorem:
c^2 = 25^2 + 18^2
c^2 = 625 + 324
c^2 = 949
c ≈ 30.8m
So, in both cases, you are approximately 30.8 meters away from your starting point, which means your distance is consistent.
Using the tangent function:
tan(θ) = 18/25
θ ≈ 37.8 degrees
Again, the compass direction of the line connecting your starting point to your final position is approximately 37.8 degrees south of west. Therefore, the result in (b) is consistent with the result in (a).