A man walks 800m on a bearing of 129°. calculate how far east he is from the starting point
You travel on a "heading".
You take a sight on a "bearing' ( eg - that lighthouse bears East by South).
Anyway East is 90 degrees so your heading is 39 degrees South of East.
Therefore the East component of your course is 800 cos 39
= 800 * 0.777
Well, if the man is walking on a bearing of 129°, it means he's not walking directly east. In fact, he's walking at a slight angle to the east. So, we cannot simply say that he is 800m east from the starting point.
But fear not, my friend! I've got a joke that might lighten the confusion:
Why don't scientists trust atoms?
Because they make up everything!
Now, back to the question at hand. To figure out how far east the man is from the starting point, we need to use a bit of trigonometry. Since he's walking at an angle to the east, we can use the cosine function to find the eastward displacement.
So, if we take the cosine of 129°, we'll find that it is about -0.4848. Now, we multiply this by the distance he walked, which is 800m:
-0.4848 x 800m = -387.84m
So, the man is approximately 387.84 meters east (or, technically, west) of the starting point.
To calculate how far east the man is from the starting point, we need to find the horizontal (east-west) component of his movement.
We can use trigonometry to calculate the east-west component. The formula for the horizontal component (x) is:
x = distance * cos(bearing)
In this case, the distance is 800m and the bearing is 129°.
Using a calculator, we find:
x = 800m * cos(129°)
x ≈ 800m * (-0.575)
x ≈ -460m
Therefore, the man is approximately 460m to the west from the starting point.
To calculate how far east the man is from the starting point, we need to determine the horizontal component of the distance he walked.
The bearing of 129° is measured clockwise from the north direction. East is 90° clockwise from the north, so we need to find the horizontal component of the 800m distance in the east direction.
To do this, we can use trigonometry. We know that the cosine of an angle in a right-angled triangle gives us the ratio of the adjacent side (in this case, the eastward distance) to the hypotenuse (in this case, the total distance walked).
Let's set up the equation:
cos(angle) = adjacent / hypotenuse
cos(129°) = adjacent / 800m
Now, we can solve for the adjacent (eastward distance):
adjacent = cos(129°) * 800m
Using a calculator, we can find the cosine of 129°, which is approximately 0.5141.
Plugging in this value, we get:
adjacent ≈ 0.5141 * 800m
adjacent ≈ 411.28m
Therefore, the man is approximately 411.28m east from the starting point.