A hiker walks 900m east and 500m south .Find the bearing of the finishing position from the staring point?
To find the bearing of the finishing position from the starting point, we need to use basic trigonometry.
1. First, let's draw a diagram to visualize the situation.
- Start by drawing a straight line representing the eastward direction and label it "900m."
- From the end point of the first line, draw a second line directly south and label it "500m."
2. Next, let's calculate the angle between the two lines.
- We can use the tangent function to find the angle.
- Tangent(theta) = opposite/adjacent = 500m/900m
- Theta = tan^(-1)(500/900)
- Using a calculator, theta ≈ 29.56°
3. Finally, the bearing is measured clockwise from the north direction.
- Since the second line is pointing south, we need to subtract the angle we calculated from 180° to get the bearing from the north.
- Bearing = 180° - 29.56° = 150.44°
Therefore, the bearing of the finishing position from the starting point is approximately 150.44°.
To find the bearing of the finishing position from the starting point, we can use trigonometry. First, let's draw a diagram to visualize the situation.
Assuming that the starting point is the origin (0,0) on a coordinate plane, the hiker walks 900m east, which means moving 900 units to the right on the x-axis. Then, the hiker walks 500m south, which means moving 500 units downward on the y-axis.
Now, we can calculate the bearing. The bearing is the angle between the line connecting the starting point and the finishing position (represented as a vector) and the positive x-axis. We can use the arctan function to find this angle.
Let's determine the coordinates of the finishing position. Since the hiker moves 900 units east and 500 units south, the finishing point has the coordinates (900, -500).
Next, we calculate the angle using the arctan function:
angle = arctan(-500/900)
Using a scientific calculator, we can find the arctan of -500/900 to be approximately -28.3 degrees.
However, since the bearing should be measured clockwise from the north direction, we need to adjust the angle.
Subtract the calculated angle from 360 degrees to get the bearing:
bearing = 360 - 28.3 = 331.7 degrees.
Therefore, the bearing of the finishing position from the starting point is approximately 331.7 degrees.
So on the Cartesian plane, it is in the fourth quadrant, with x-y as (900,-500).
Atan(-500/900)= -29° approximately.
So the bearing is S61°E.