if a man walks 700 m on a bearing of 040"how far east is he from his starting point
d = 700*Cos A.
To determine how far east the man is from his starting point, we need to break down the bearing angle of 040° into its horizontal and vertical components.
First, let's identify the horizontal component, which represents the eastward movement. To find this component, we need to use trigonometry.
The horizontal component can be calculated using the formula:
Horizontal component = Distance × cos(Bearing angle)
Given that the distance traveled by the man is 700 m, and the bearing angle is 040°, we can substitute these values into the formula:
Horizontal component = 700 m × cos(40°)
Using a scientific calculator or a trigonometric table, we find that cos(40°) is approximately 0.766.
Substituting this value into the formula:
Horizontal component ≈ 700 m × 0.766
Horizontal component ≈ 536.2 m
Therefore, the man is approximately 536.2 meters east of his starting point.
To determine how far east the man is from his starting point, we can use the concept of trigonometry and convert the bearing angle into a meaningful measure.
1. Convert the bearing angle from the sexagesimal system to decimal degrees:
- The given bearing angle is 040".
- To convert to decimal degrees, divide the number of seconds by 60 (since there are 60 seconds in a minute).
- 040" / 60 = 0.67.
2. Determine the eastward component of the man's movement:
- Since the bearing is measured from the north and the man walks in the east direction, we need to consider the cosine function.
- The eastward component is calculated by multiplying the total distance the man walks (700 m) by the cosine of the converted bearing angle (0.67):
- Eastward component = 700 m * cos(0.67°).
3. Calculate the eastward component:
- Using a scientific calculator, find the cosine of 0.67 degrees.
- Multiply the result by 700 m to get the eastward component.
By following these steps, you will find the exact distance east the man is from his starting point.