(a). 0.47623.

(b). 0.25412.

To convert radians to degrees divide by and multiply by 180. So, 0.47623 divided by and multiplied by 180 gives 27.286°. You can convert the fractions of a degree to minutes and seconds as follows. Multiply the fraction by 60 to get the number of minutes. Here, 0.286 times 60 equals 17.16, so the angle could be written as 27° 17.16′. Then take any fraction of a minute that remains and multiply by 60 again to get the number of seconds. Here, 0.16 times 60 equals about 10, so the angle can also be written as 27° 17′ 10″.

(a). 27° 17′ 10″.

(b). 14.56° = 14°33.6′ = 14°33’36”.

2) How much does one change latitude by walking due north one mile, assuming the earth to be a sphereof radius 3956 miles?

***You’ve got a circle of radius 3956 miles and an arc of that circle of length 1 mile. What is the angle in degrees? (The mean radius of the earth was known fairly accurately in 1914. See if you can find out what Eratosthenes thought the radius of the earth was back in the third century B.C.)

Angle = 1/3956 = 0.0002528 radians = 0.01448° = 0.8690′ = 52.14″.

3) Comput ethe high lengh of one minute of arc on a great circle of the earth. How long is the length of one second of arc?

***A minute of arc is 1/60 of a degree. Convert to radians. The radius is 3956. What is the length of the arc?

One minute = 0.0002909 radians. 1.15075 miles = 6076 feet. Therefore one second will correspond to 101.3 feet.

http://www.clarku.edu/~djoyce/trig/angle.html

(a) 0.47623r

= 180 * 0.47623 / pi deg.

= 27d 17m 9.49s.

(b) 0.25412r

= 180 * 0.25412 / pi deg

= 14d 33m 36.01s.

2.

180 * 3600 / 3956pi

= 52.14sec.

3.

1 min

= pi * 3956 / (180 * 60)

= 1.151mi.

1 sec

= 1.151 / 60

= 1.198 * 10^(-2) mi.