The positions T and U are (40degreesN,84degreesE)and U(40degreesN,96degreesW).calculate the distance between them(take pie=3.142)

Answer 1

To calculate the distance between points T and U, we can use the spherical law of cosines formula:

cos(d) = sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 - lon1)

where lat1 and lon1 are the coordinates of point T (40 degrees N, 84 degrees E) and lat2 and lon2 are the coordinates of point U (40 degrees N, 96 degrees W).

First, we need to convert the longitudes to positive values since the formula works with positive values:

Lon1 = 84 degrees E
Lon2 = 360 - 96 = 264 degrees E

Now, we can plug in the values into the formula:

cos(d) = sin(40) * sin(40) + cos(40) * cos(40) * cos(264 - 84)

cos(d) = sin(40) * sin(40) + cos(40) * cos(40) * cos(180)

cos(d) = sin(40) * sin(40) + cos(40) * cos(40) * -1

cos(d) = 0.6428 * 0.6428 + 0.766 * 0.766 * -1

cos(d) = 0.4129356432 - 0.5878976

cos(d) = -0.1749619568

Now, we can calculate the distance:

d = arccos(-0.1749619568)

d = 98.99 degrees

Now, we can convert the angle distance into miles using the circumference of the Earth:

1 degree of longitude = circumference of Earth / 360 degrees
1 degree of longitude = 24901 miles / 360 degrees
1 degree of longitude = 69.17 miles

Hence, the distance between points T and U is approximately 98.99 degrees * 69.17 miles/degree = 6845.98 miles.