A girl walks 800meters on a bearing of 129degrees calculate how far east and south is from her starting point
I made a sketch on an x-y grid, and it shows her ending up in the 4th quadrant
at (800cos39°, 800sin39°) or (.... , .....)
All angles are measured CW from +y-axis.
D = 800m[129o] = 800*sin129+800*cos129 = 622-503i.
D = 622 m. East and 503 m South.
To determine how far east and south the girl is from her starting point, we can use trigonometry.
First, let's break down the 129-degree bearing into its east-west and north-south components.
The bearing of 129 degrees can be measured from the north in a clockwise direction. This means that the girl is heading southeast since 129 degrees is between 90 degrees (east) and 180 degrees (south).
Now, let's calculate the eastward and southward components of the distance.
To find the eastward component, we can use cosine because it relates to the adjacent side in a right triangle. The formula is:
Eastward distance = Total distance * cosine(bearing angle)
Eastward distance = 800 * cos(129 degrees)
Next, calculate the southward component using sine, which relates to the opposite side in a right triangle:
Southward distance = Total distance * sine(bearing angle)
Southward distance = 800 * sin(129 degrees)
Now, let's compute these values:
Eastward distance = 800 * cos(129 degrees) ≈ -343.77 meters (rounded to two decimal places)
Southward distance = 800 * sin(129 degrees) ≈ -713.72 meters (rounded to two decimal places)
Remember that the negative signs indicate that the girl is east and south of her starting point. So, she is approximately 343.77 meters east and 713.72 meters south from her starting point.