find the distance between the cities,,assume that thee earth is a sphere radius of 4000 miles at that cities are on same longitude, one city is due north of the order,,,San Francisco California has 37 degree 47'36" while Seattle,Washington 47 degree 37'18"

the cities are 9°49'42" apart.

The full circumference is 8000π miles, and 360°

so, the distance is

(9°49'42")/360° * 8000π miles

...

To find the distance between two cities when they are on the same longitude and assuming that the Earth is a sphere with a radius of 4000 miles, you can use the formula for calculating the distance on a sphere using the longitude and latitude coordinates.

The formula to calculate the distance between two points on a sphere is:

distance = radius * arccos(sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(long2 - long1))

Where:
- radius is the radius of the Earth (in this case, 4000 miles)
- sin and cos are trigonometric functions
- lat1 and lat2 are the latitude coordinates of the two cities in radians
- long1 and long2 are the longitude coordinates of the two cities in radians

First, you need to convert the given latitude and longitude coordinates from degrees, minutes, and seconds to decimal degrees:

San Francisco, California:
- Latitude (lat1): 37 degrees 47' 36" = 37 + (47/60) + (36/3600) = 37.79333 degrees
- Longitude (long1): Same longitude as Seattle, Washington due north, so no calculation needed

Seattle, Washington:
- Latitude (lat2): 47 degrees 37' 18" = 47 + (37/60) + (18/3600) = 47.62167 degrees
- Longitude (long2): Same longitude as San Francisco, California, so no calculation needed

Now, let's plug the converted values into the formula:

distance = 4000 * arccos(sin(37.79333) * sin(47.62167) + cos(37.79333) * cos(47.62167) * cos(0))

Calculating this equation will give you the distance between the two cities in miles.