Question

The measure of angle 6° radian in degrees is
1. 343°39'11"
2. 343°38'11"
3. 343°38'12"
4. 343°35'11"

Answer 1

Correct Answer - Option 2 : 343°38'11"

Concept:

The conversion from radian to a degree is:

\(\rm \frac {D}{180} = \frac {C}{\pi}\)

Calculation:

Given: 6°

\(\rm {D} = \frac {180 \ \times \ 6}{\pi} = \frac {1080\ \times \ 7}{22}\)

⇒ \(\rm D = 343 \frac {7}{11}degree = 343 + \frac {(7 \ \times \ 60)}{11} Minutes\)       (∵1°  = 60')

⇒ 343° + 38' + \(\rm 2\over11\) Minutes                                   (∵ 1' = 60")

⇒ 343° + 38' + 10.9"

⇒ 343°38'11"

6° Radian = 343°38'11"