Find the length of the parallels of latitude 42 degree north
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at latitude d, the radius of the cross-section of earth is
r = R cos(d)
where R is the radius at the equator.
So, the circumference there is 2pi*r
To find the length of the parallels of latitude at 42 degrees north, you can use the formula for the length of degrees of latitude:
Length of 1 degree of latitude = (pi/180) * radius of the Earth
The radius of the Earth is approximately 6,371 kilometers.
So, the length of 1 degree of latitude = (pi/180) * 6,371 kilometers = 111.32 kilometers.
Now, to find the length of the parallels of latitude at 42 degrees north, you can multiply the length of 1 degree of latitude by the number of degrees:
Length of parallels of latitude at 42 degrees north = 111.32 kilometers/degree * 42 degrees
Calculating this:
Length of parallels of latitude at 42 degrees north = 4670.24 kilometers
To find the length of the parallels of latitude, we can use the formula:
Length of a parallel of latitude = (circumference of the Earth * cos(latitude))
The circumference of the Earth is approximately 40,075 kilometers.
Plugging in the given latitude of 42 degrees north into the formula:
Length of a parallel of latitude = (40,075 km * cos(42 degrees))
To find the value of cos(42 degrees), we can use a scientific calculator or an online trigonometric calculator.
Cosine function uses radians as the input, so we need to convert 42 degrees to radians:
42 degrees = (42 * π) / 180 radians
Now, we plug this value into the cosine function:
Length of a parallel of latitude = (40,075 km * cos((42 * π) / 180 radians))
Calculating this expression will give us the length of the parallel of latitude at 42 degrees north.