Suppose you walk 18.0m straight west and then 25.0 north. How far are you from your starting point and what is the compass direction of a line connecting your startting point to your final position?
d=sqrt(18²+25²)=...
tanα=18/25,
α= arctsn(18/25)
To find the distance and the compass direction, we can use the Pythagorean theorem and trigonometric functions.
Step 1: Calculate the distance traveled in the west direction (x-axis) by walking 18.0m straight west. Since you only move in one dimension, the distance in the west direction is simply 18.0m.
Step 2: Calculate the distance traveled in the north direction (y-axis) by walking 25.0m straight north. Again, since you only move in one dimension, the distance in the north direction is simply 25.0m.
Step 3: Use the Pythagorean theorem to find the total distance from your starting point. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance in the west direction (18.0m) is one side of the triangle, and the distance in the north direction (25.0m) is the other side. The hypotenuse of the triangle is the total distance from the starting point.
Using the Pythagorean theorem, we have:
Total distance^2 = (distance in the west direction)^2 + (distance in the north direction)^2
Total distance^2 = (18.0m)^2 + (25.0m)^2
Total distance^2 = 324m^2 + 625m^2
Total distance^2 = 949m^2
Taking the square root of both sides gives us:
Total distance = √949m
Total distance ≈ 30.8m (rounded to the nearest tenth)
Therefore, the distance from your starting point is approximately 30.8m.
Step 4: To find the compass direction of the line connecting the starting point to the final position, we can use trigonometric functions. In this case, we can use the inverse tangent function (arctan) to find the angle.
Using the formula:
Angle = arctan(distance in the north direction / distance in the west direction)
Angle = arctan(25.0m / 18.0m)
Angle ≈ 53.1 degrees (rounded to the nearest tenth)
Therefore, the compass direction of the line connecting your starting point to your final position is approximately 53.1 degrees north of west.