Distance And Angle Measurement

We know that

1%20%5Ctext%7B%20radian%7D%20%3D%20%5Cfrac%7B180%5E%5Ccirc%7D%7B%5Cpi%7D

. Using the approximate value

%5Cpi%20%5Capprox%203.1416

, we get:

1%20%5Ctext%7B%20radian%7D%20%3D%20%5Cfrac%7B180%5E%5Ccirc%7D%7B3.1416%7D%20%5Capprox%2057.2958%5E%5Ccirc.

Converting the decimal part

0.2958

into minutes and seconds:

0.2958%5E%5Ccirc%20%5Ctimes%2060%20%3D%2017.748'%20%5Cquad%20%5Ctext%7B(minutes)%7D%2C

0.748%20%5Ctimes%2060%20%3D%2044.88''%20%5Cquad%20%5Ctext%7B(seconds)%7D.

Thus,

1%20%5Ctext%7B%20radian%7D%20%5Capprox%2057%5E%5Ccirc%2017'%2045''

, which is the correct answer (D).

Chapter Questions
1 MCQs