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
4.19 cos 10.4
To solve this problem, we can break it down into two components: the north-south component and the east-west component.
First, let's focus on the person who walks 10.4 degrees north of east for 4.19 km. Since the person is walking at an angle, we can compute the north-south and east-west components using trigonometry.
The north-south component can be found by multiplying the distance traveled (4.19 km) by the sine of the angle (10.4 degrees). Let's call this component A.
A = 4.19 km * sin(10.4 degrees)
The east-west component can be found by multiplying the distance traveled (4.19 km) by the cosine of the angle (10.4 degrees). Let's call this component B.
B = 4.19 km * cos(10.4 degrees)
Now, let's consider the second person who walks due north, then due east. We want to find how far this person would walk due east to arrive at the same location.
Since the first person's north-south displacement is the same as the second person's north-south displacement, we can use the value of component A we calculated earlier.
For the second person, since they walk due north, their north-south displacement is equal to the distance traveled. In other words, the second person's north-south component is 4.19 km.
Since the second person walks due east to arrive at the same location, we need to find their east-west displacement. Let's call this distance X.
To find X, we can use the Pythagorean theorem:
X^2 = (distance traveled by the second person)^2 - (north-south component)^2
X^2 = (4.19 km)^2 - (4.19 km * sin(10.4 degrees))^2
Solving this equation will give us the value of X, which is the distance the second person would walk due east.