Western hemisphere:
A topographic quadrangle is a 30' series map (it covers 30' longitude and latitude). If the western longitude boundary is 120 degrees 02 feet 30 inches, what is the longitude of the eastern boundary?
See my answer below.
To find the longitude of the eastern boundary, we need to determine the width of the topographic quadrangle, which is the difference between the western and eastern longitudes.
To calculate this difference, we need to convert the longitude from degrees, minutes, and seconds to a decimal value.
First, let's convert 02 feet and 30 inches to decimal values:
Since 1 foot is equal to 12 inches, we can convert 02 feet to inches: 02 feet * 12 inches/foot = 24 inches
Next, we add the 30 inches to the previous result: 24 inches + 30 inches = 54 inches
To convert inches to decimal feet, we divide the inches by 12: 54 inches / 12 inches/foot = 4.5 feet
Now we sum up the converted values to get the total longitude in feet: 120 degrees * 60 minutes/degree * 60 seconds/minute + 2 feet * 12 inches/foot + 30 inches/12 inches/foot = 120 * 60 * 60 + 24 + 4.5 = 432,084.5 feet
Since 1 degree of longitude is equal to 364,567.2 feet, we can divide the total longitude by this value to get an approximate longitude in degrees: 432,084.5 feet / 364,567.2 feet/degree = 1.1869 degrees
Now, to find the longitude of the eastern boundary, we subtract the approximate longitude in degrees from the longitude of the western boundary:
120 degrees 02 feet 30 inches - 1.1869 degrees = 118.8131 degrees
Therefore, the longitude of the eastern boundary is approximately 118.8131 degrees.