A man walks 800km on a bearing of 129 degree. How far is he due east from the starting point?
that course will put him
800 cos(90-129)° = 800 cos39° east
X = 800*sin129 = 621.7 km, East.
To find out how far the man is due east from the starting point, we need to determine the component of his displacement in the east direction.
We can break down the displacement into two components: one in the north-south direction and the other in the east-west direction. The bearing of 129 degrees gives us the angle between the displacement vector and due north.
To find the east-west component, we'll use trigonometry.
The east-west component is given by: east-west displacement = displacement * cos(angle)
Here's how to calculate it:
1. Convert the bearing angle to radians:
angle_rad = 129 * (π/180)
2. Calculate the east-west displacement:
east_west_displacement = 800 km * cos(angle_rad)
Using a scientific calculator or software, let's find the value of cos(angle_rad):
cos(129 * (π/180)) ≈ -0.64278760968
Now, calculate the east-west displacement:
east_west_displacement = 800 km * (-0.64278760968)
east_west_displacement ≈ -514.23 km
Since we are interested in the distance towards the east, we take the absolute value of the east-west displacement:
east_displacement = |east_west_displacement| ≈ |-514.23 km| ≈ 514.23 km
Therefore, the man is approximately 514.23 km due east from the starting point.