A person walks 10.4 degrees north of east for 4.19 km. Another person walks due north, then due east to arrive at the same location. How far would this person walk due east? Answer in units of km
D = 4.19*Cos10.4
To find the distance the second person would walk due east, we can use trigonometry.
First, let's draw the path of the first person. They walk 10.4 degrees north of east for 4.19 km.
Now, let's break down the motion of the second person. They walk due north, and then due east to arrive at the same location.
Since the two people end up at the same location, we can see that the second person has formed a right triangle with the initial eastward path of the first person being the hypotenuse.
The angle between the initial eastward path and the due east direction of the second person is 90 - 10.4 = 79.6 degrees (as the total of all angles in a triangle is 180 degrees).
Now, using trigonometry, we can determine the distance the second person walks due east. We have the hypotenuse (4.19 km) and the angle between the hypotenuse and the adjacent side (79.6 degrees).
Using the cosine function:
cos(79.6 degrees) = adjacent / hypotenuse
We can rearrange this equation to solve for the adjacent side:
adjacent = hypotenuse * cos(79.6 degrees)
Substituting in the values, we get:
adjacent = 4.19 km * cos(79.6 degrees)
Calculating this, we find:
adjacent ≈ 0.852 km
Therefore, the second person would walk approximately 0.852 km due east to arrive at the same location.