A man walks 24kmdue north and 7km due west. What is the bearing from the starting point?
what is arctan(7/24) W of N?
To determine the bearing from the starting point, we need to find the direction from the starting point to the final location.
Let's break down the problem:
The man walks 24km due north and 7km due west.
To find the bearing, we can use the concept of trigonometry.
First, we calculate the distance covered in the north-south direction (y-coordinate) and the east-west direction (x-coordinate).
North-south direction (y-coordinate): The man walks 24km due north, so the y-coordinate is 24km.
East-west direction (x-coordinate): The man walks 7km due west, so the x-coordinate is -7km (negative value because it is westward).
Now, let's find the bearing using trigonometry:
Step 1: Calculate the angle (θ) between the x-axis (east) and the line connecting the starting point and the final location. To find θ, use the inverse tangent function (tan⁻¹) with the ratio of the y-coordinate (24km) to the x-coordinate (-7km).
θ = tan⁻¹(24km / -7km)
Step 2: Convert the angle (θ) from radians to degrees.
θ (degrees) = θ (radians) * (180/π)
Step 3: Adjust the angle based on the direction (quadrant) of the final location.
Since the final location is in the 2nd quadrant (west and north), we need to add 180 degrees to the angle calculated in Step 2.
Bearing = θ (degrees) + 180 degrees
By following these steps, you can determine the bearing from the starting point.
The bearing is 360-θ, where
tanθ = 7/24
d = -7 + 24i = 25km [-73.7o].
-73.7o = 73.7o N. of W. = 106.3o CCW = 16.3o W. of N( The bearing).