Find the parallel of latitude along a journey of 166 km makes a change of 4 degrees in longitude .
The earth's radius is 6378 km
at a latitude of θ, the radius is 6378 cosθ
So, you want
6378 cosθ * 4/360 * 2π = 166
θ = 68.1°
Why did the parallel of latitude go on a journey? Because it wanted to see if it could find a longitude soulmate!
But let me help you answer this seriously. We can calculate the parallel of latitude by using the formula:
ΔLongitude = Dist × cos(Latitude) × 2π/360
Where ΔLongitude is the change in longitude, Dist is the total distance traveled, and Latitude is the initial latitude.
In this case, we have ΔLongitude = 4 degrees and Dist = 166 km. Now we just need to find the latitude. Unfortunately, you haven't provided the latitude information, so I can't give you a precise answer.
If you provide the initial latitude, I'd be happy to crunch the numbers for you and give you a proper response that's out of this world!
To find the parallel of latitude along a journey of 166 km that makes a change of 4 degrees in longitude, we can use the concept of longitude and the Earth's circumference.
Step 1: Determine the Earth's circumference
The Earth's circumference is approximately 40,075 km.
Step 2: Calculate the change in longitude per kilometer
To calculate the change in longitude per kilometer, we divide the Earth's circumference by 360 degrees:
Change in longitude per kilometer = 360 degrees / 40,075 km
Step 3: Calculate the change in longitude for the given journey
The change in longitude for the given journey of 166 km is:
Change in longitude = Change in longitude per kilometer * Journey distance
Change in longitude = (360 degrees / 40,075 km) * 166 km
Step 4: Calculate the latitude change for a 4-degree longitude change
To find the latitude change for a given longitude change, we need to know the distance between each parallel of latitude. The distance between each parallel of latitude is constant and can be calculated using the Earth's circumference.
Distance between each parallel of latitude = Earth's circumference / 360 degrees
Step 5: Calculate the latitude change for the given change in longitude
The latitude change for the given change in longitude can be calculated as:
Latitude change = Distance between each parallel of latitude * (Change in longitude / 4 degrees)
Substituting the values we calculated earlier:
Latitude change = (Earth's circumference / 360 degrees) * ((360 degrees / 40,075 km) * 166 km / 4 degrees)
Simplifying the equation:
Latitude change = (166 km / 40,075 km) * 166 km
Calculating the latitude change:
Latitude change = 0.4136 degrees
Therefore, the parallel of latitude along the journey of 166 km that makes a change of 4 degrees in longitude is approximately 0.4136 degrees.
To find the parallel of latitude along a journey of 166 km that makes a change of 4 degrees in longitude, we can use the formula:
Distance on Earth's surface = Radius of Earth * Change in latitude * Conversion factor
1. First, we need to determine the radius of the Earth, which is approximately 6371 km. Let's convert it to the same unit as the given distance (166 km), in this case, kilometers.
Radius of Earth = 6371 km
2. Next, we need to determine the conversion factor to convert degrees to kilometers. The circumference of the Earth at the equator is approximately 40,075 km, and it represents 360 degrees.
Conversion factor = Circumference of Earth at the Equator / 360
= 40075 km / 360
= 111.319 km
3. Now we can calculate the change in latitude using the formula:
Change in latitude = Distance on Earth's surface / (Radius of Earth * Conversion factor)
= 166 km / (6371 km * 111.319 km)
≈ 0.0247 degrees
Therefore, the parallel of latitude along a journey of 166 km that makes a change of 4 degrees in longitude is approximately 0.0247 degrees of latitude.