an ant walk 1 meter west and then 3 meters north whats is the ants direction in degrees
To find the ant's direction in degrees, we can use basic trigonometry. We need to calculate the angle between the displacement of the ant (horizontal and vertical) and the positive x-axis.
1. Draw a diagram: Start by visualizing the ant's movement. Draw a horizontal line of 1 meter in the negative x-direction and a vertical line of 3 meters in the positive y-direction. Connect the starting point with the end point to form a right-angled triangle.
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2. Calculate the angle: To find the angle between the displacement and the positive x-axis, we need to use the inverse tangent function (arctan).
angle = arctan(opposite / adjacent)
In this case, the opposite side is 3 meters (the vertical line) and the adjacent side is 1 meter (the horizontal line). So,
angle = arctan(3 / 1)
Using a scientific calculator or an online trigonometry tool, we can find:
angle ≈ 71.57 degrees (rounded to two decimal places)
Therefore, the ant's direction is approximately 71.57 degrees from the positive x-axis.
arctan(3) = 71.6 degrees north of west, relative to the starting point.
One metre west and 3 metres north will be equivalent to an angle of tan-1(1/3) west of north.
Use a calculator or a table of tangents to find the angle.