find the parralel of latitude along which a journey of 166km makes a change of 4 degree in longitude give answer to the nearest degree
4 degrees = 1/90 of circumference
radius at latitude θ = r cosθ
r of earth is 6378 km
circumference at latitude θ is 2π*6378 cosθ
we want 1/90 (2π*6378 cosθ) = 116
so,
cosθ = (116*90)/(2π*6378) = 0.26
θ = 75°
Well, that sounds like quite the journey! If a distance of 166 km corresponds to a change of 4 degrees in longitude, then we can calculate the parallel of latitude using some clownish mathematics.
One degree of longitude at the equator roughly corresponds to a distance of 111 km. So, if a change of 4 degrees in longitude equals 166 km, we can say that each degree corresponds to 166 km divided by 4, which equals 41.5 km.
Now, here comes the punchline. Since we're looking for the parallel of latitude, and each degree of latitude is always a constant distance of about 111 km apart, we can divide 41.5 km by 111 km per degree.
Doing the math, we find that the change of 4 degrees in longitude is approximately equivalent to 0.373 degrees of latitude. So, to find the parallel of latitude, we take a wild guess and round to the nearest degree.
Therefore, the parallel of latitude is approximately 0 degrees. But, of course, this calculation is just for laughs and shouldn't be taken seriously.
To find the parallel of latitude along which a journey of 166 km makes a change of 4 degrees in longitude, we can use the formula:
Distance in longitude = 2 * π * R * (Δlongitude / 360)
where:
- Distance in longitude is the distance traveled in terms of longitude.
- R is the radius of the Earth, which is approximately 6,371 km.
- Δlongitude is the change in longitude.
Rearranging the formula to solve for the parallel of latitude gives us:
Latitude = (Distance in longitude * 360) / (2 * π * R)
Now we can plug in the values:
Δlongitude = 4 degrees
Distance in longitude = 166 km
R ≈ 6,371 km
Latitude = (4 * 360) / (2 * π * 6,371) ≈ 0.225
To find the nearest degree, we can simply round the latitude to the nearest whole number:
Latitude ≈ 0
Therefore, the parallel of latitude along which a journey of 166 km makes a change of 4 degrees in longitude is approximately 0 degrees.
To find the parallel of latitude along which a journey of 166 km makes a change of 4 degrees in longitude, we need to determine the distance on the Earth's surface covered by each degree of longitude.
The Earth's equator has a circumference of approximately 40,075 km. Since there are 360 degrees of longitude around the Earth, each degree of longitude covers a distance of 40,075 km / 360 = 111.32 km.
Now, we can calculate the latitude where a journey of 166 km makes a change of 4 degrees in longitude. We divide the distance traveled (166 km) by the distance covered by each degree of longitude (111.32 km/degree):
166 km / 111.32 km/degree ≈ 1.49 degrees
Therefore, a journey of 166 km makes a change of approximately 1.49 degrees in latitude.
To find the parallel of latitude, we need to consider whether this change in latitude is north or south of a given starting point. Without knowing the starting point, we cannot provide an exact parallel of latitude. However, we can give you the approximate answer.
If the given starting point is in the Northern Hemisphere, then the parallel of latitude will be around 1.49 degrees north.
If the given starting point is in the Southern Hemisphere, then the parallel of latitude will be around 1.49 degrees south.
Please note that this is an approximation, and the exact parallel of latitude will depend on the starting point.