Question

How to convert 2.5 radian to degree and minute and second $ ? $

Answer 1

Hint: To convert the radian to degree multiplying to the given number which is in radian the resultant number will be in degree then to convert degree to minute by multiplying 60’ to the given number which is in degree the resultant number will be in minute and to convert minute to second by multiplying 60’’ to the given number which is in minute the resultant number will be in second.

Complete step-by-step answer:
Radians and degrees are both units used for measuring angles. As you may know, a circle consists of $ 2\pi $ radians, which is the equivalent of $ {360^ \circ } $ both of these values represent going once around a circle. Therefore, $ 1\,\pi $ radian represents going $ {180^ \circ } $ around a circle, which makes $ \dfrac{{180}}{\pi } $ the perfect conversion tool for moving from radians to degrees. To convert from radians to degrees, you simply have to multiply the radian value by $ \dfrac{{180}}{\pi } $ . Next, one degree (°) is equal to 60 minutes (') and equal to 3600 seconds ("): 1° = 60' = 3600" , to convert decimal degrees to minutes multiplying 60 to the decimal degree number and next to convert decimal minute to second by multiply 60 to the decimal minute.
Here in the question given 2.5 radian
Firstly, we convert radian to degree i.e., multiply by $ \dfrac{{180}}{\pi } $
 $ \Rightarrow \,\,2.5 \times \dfrac{{180}}{\pi } $
The value of $ \pi $ is 3.14
 $ \Rightarrow \,\,2.5 \times \dfrac{{180}}{{3.14}} $
 $ \Rightarrow \,\dfrac{{450}}{{3.14}} $
 $ = \,{143.31^ \circ } $
Next, we convert decimal degree $ {0.31^ \circ } $ multiply by 60
 $ \Rightarrow \,\,\,0.31 \times 60 $
 $ = \,\,18.6' $
At lastly, we convert decimal minute $ 0.6' $ multiply by 60
 $ \Rightarrow \,\,\,0.6 \times 60 $
 $ = \,\,36'' $
Hence, 2.5 radian = $ {143^ \circ }18'36'' $
So, the correct answer is “ $ {143^ \circ }18'36'' $ ”.

Note: We can change the number from one form to another. We have a specific method to convert the numbers. Here in this question, we have converted the given number which is in radian to the degree and to the minute and to the second. For the conversion we have followed the methods as shown above.