a student wals 5km due north from O and then 8km due east find his bearing from O
N arctan(8/5)° E
To find the bearing of the student from point O, we can use trigonometry.
First, let's draw a diagram to visualize the situation:
N (O)
|
|
|
--------X---------
|
|
|
The point N represents the starting position, O represents the reference point, and X represents the ending position of the student after walking 5km due north and then 8km due east.
Now, let's calculate the bearing:
1. Calculate the angle between the reference line and the line connecting the reference point O with the ending point X. This will give us the direction from O to X.
- To find this angle, we can use the tangent function:
tangent(theta) = (opposite side) / (adjacent side)
N (O)
theta = arctan | => theta = arctan(8/5)
X
Using a calculator or trigonometric tables, we find that theta is approximately 57.99 degrees.
2. Convert the angle from Step 1 to bearing format. Bearing is measured from the north line in a clockwise direction.
- Subtract the angle obtained in Step 1 from 90 degrees to get the bearing in the northern hemisphere.
bearing = 90 - theta
= 90 - 57.99
= 32.01 degrees
Therefore, the student's bearing from point O is approximately 32.01 degrees.