a girl walks 800 m on a bearing of 129 degrees.calculate how far east and south she is from her starting point.
you will be in the 4th quadrant, 39° down from the x-axis
cos 39° = x/800
x = 800cos39 = 621.7 m east
y = 800sin39 = 503.5 m south
notice :
621.7^2 + 503.5^2 = 639979.1489
√639979.1489 = 799.987 , not bad
To calculate how far east and south the girl is from her starting point, we can use trigonometry.
First, let's break down the information given:
- The girl walks 800 meters, which is the hypotenuse of a right triangle.
- The bearing of 129 degrees indicates the angle between her walking direction and due north.
To calculate how far east and south she is, we need to use the angles in the right triangle formed by her direction and due north.
Step 1: Calculate the angle between her walking direction and due east.
The angle between due north and due east is 90 degrees. Given that her bearing is 129 degrees, we can subtract 90 degrees from her bearing:
129 degrees - 90 degrees = 39 degrees
The angle 39 degrees represents the angle between her walking direction and due east.
Step 2: Use trigonometry to calculate the distance east and south.
We can use the cosine function to calculate the distance east and the sine function to calculate the distance south.
Distance East = 800 meters * cos(39 degrees)
Distance South = 800 meters * sin(39 degrees)
Calculating the values:
Distance East = 800 meters * cos(39 degrees) = 608.61 meters
Distance South = 800 meters * sin(39 degrees) = 504.85 meters
Therefore, the girl is approximately 608.61 meters east and 504.85 meters south from her starting point.