A man walks 800 meters on a bearing of 129 degrees.Calculate how far east he is from his starting point.
180-129 equal to 39
After you make a sketch you should see that
distance = 800cos39°
= ...
To calculate how far east the man is from his starting point, we need to find the vertical component of the distance he walked, since the bearing of 129 degrees is measured clockwise from the north.
To do this, we can use trigonometry. We know that the opposite side of a right triangle represents the vertical distance, and the hypotenuse represents the total distance walked (800 meters). Using the sine function, we can find the vertical component (east-west distance) by multiplying the total distance walked by the sine of the angle.
First, let's convert the bearing to radians:
129 degrees = 129 * π/180 = 2.25 radians
Now, apply the sine function to find the vertical component:
Vertical component = 800 meters * sin(2.25 radians)
Using a calculator, we can find that sin(2.25) ≈ 0.919
Therefore, the vertical component (east-west distance) is approximately:
Vertical component = 800 meters * 0.919 ≈ 735.2 meters
The man is approximately 735.2 meters east from his starting point.