A person walks 25 degree north of east for 31 km. How far would the person walk due north and due east to arrive at the same location?
N= 31sin25
E=31cos25
make certain you draw the diagram, and reason this out.
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To find out how far the person would walk due north and due east to arrive at the same location, we can break down the given direction and distance into its north and east components.
Given:
Angle walked = 25 degrees north of east
Distance walked = 31 km
First, let's break down the given angle walked into its eastward and northward components.
Step 1: Calculate the eastward component
The eastward component is the cosine of the angle multiplied by the distance.
Eastward component = cos(angle) * distance
Eastward component = cos(25°) * 31 km
Step 2: Calculate the northward component
The northward component is the sine of the angle multiplied by the distance.
Northward component = sin(angle) * distance
Northward component = sin(25°) * 31 km
To calculate the northward and eastward components of the given angle, we can use a calculator or a tool such as a scientific calculator or trigonometry tables.
Step 3: Calculate the distances due north and due east
The distances due north and due east can be found using the eastward and northward components.
Distance due north = Northward component
Distance due east = Eastward component
Substituting the calculated values into the equations:
Distance due north = sin(25°) * 31 km
Distance due east = cos(25°) * 31 km
Now, we can calculate the values using a calculator:
Distance due north ≈ sin(25°) * 31 km ≈ 13.32 km (rounded to two decimal places)
Distance due east ≈ cos(25°) * 31 km ≈ 28.03 km (rounded to two decimal places)
Therefore, to arrive at the same location, the person would need to walk approximately 13.32 km due north and 28.03 km due east.