Convert 11 pi3 radius to degrees Find the central angle thet

Convert 11 pi/3 radius to degrees. Find the central angle theta of a circle with radius 5 that subtends an arc of length 10. Pittsburgh and Miami lie approximately on the same longitude line (that is, a great circle of the earth). Pittsburgh bas a between the two cities if the radius has a latitude of 25.5 degree N. Find the distance between the two cities if the radius of the earth is 3960 miles.

Solution

Solution:(3)

There is a formula that relates the arc length of a circle of radius, r, to the central angle , in radians.

S = r

If \" s \" is length of the arc of a circle with radius = r, then the central angle [ angle in radians subtended by the arc at the center ( ) ] is --

=> = ( Arc length ) divided by radius.

=> = 10/5 Radians = 2 Radians

or

=> = 2 (180/ ) degrees = (360/ ) degrees = 114.59 degree

Solution: (4)

If the radius of the earth is 3960 miles then we know that the circumference is 2r
2 * 3.14159265 * 3960 = 24,880 miles

The total circumference is covered by 360 degrees
The difference of the two latitudes is 15 degrees
15/360 * 24,880 = 1037 miles