A man walks 800m on a bearing of 129 degree, calculate how Far East he is from his starting point

Question

A man walks 800m on a bearing of 129 degree, calculate how Far East he is from his starting point

Answer 1

800 cos(90-129)°

Answer 2

To determine how far east the man is from his starting point, we need to calculate the horizontal component of the displacement.

Step 1: Identify the bearing angle and convert it to a direction angle:

The bearing angle is given as 129 degrees. However, since bearing angles are usually measured from the north direction, we need to convert it to the direction angle measured from the east direction.

Since the east direction is 90 degrees clockwise from the north direction, we subtract 90 degrees from the given bearing angle:

Direction angle = 129 degrees - 90 degrees = 39 degrees

Step 2: Calculate the horizontal component of the displacement:

Using trigonometry, we can determine the horizontal component of the displacement using the formula:

Horizontal component = Displacement * cos(Direction angle)

Given:
Displacement = 800m
Direction angle = 39 degrees

Horizontal component = 800m * cos(39 degrees)

Now, we can calculate the horizontal component:

Horizontal component ≈ 800m * 0.766 = 612.8m

Therefore, the man is approximately 612.8 meters east from his starting point.

Answer 3

To calculate how far east the man is from his starting point, we can break down the problem into its eastward and northward components.

First, we need to find the eastward distance traveled by the man. To do this, we need to calculate the eastward projection of the 800m distance.

Since the bearing is given as 129 degrees, we can visualize it as an angle measured from the north, turning clockwise.

The eastward projection can be calculated using trigonometry. The cosine of an angle represents the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, the angle is 129 degrees, and the hypotenuse is the distance traveled (800m). Therefore, the eastward distance can be calculated as follows:

Eastward distance = cos(129°) × 800m

Using a calculator or a trigonometric table, we find that cos(129°) is approximately -0.577. Therefore:

Eastward distance ≈ -0.577 × 800m
Eastward distance ≈ -461.6m

Note that the result is negative, indicating that the man is west of his starting point. Therefore, we need to take the absolute value to get the distance east:

Eastward distance ≈ | -461.6m |
Eastward distance ≈ 461.6m

So, the man is approximately 461.6 meters east of his starting point.