Question

find the radian measure corresponding to 5°37' 30"

Answer 1

Our angle is = 5° 37' 30"

For 30''

We know 1' = 60''

So, 30'' = 1/60 * 30 = 0.5'

So our angle will be = 5° 37.5'

Now we know, 1° = 60'

So, 37.5' = 1/60 * 37.5 = 0.625°

So our angle is = 5.625°

To convert the angle into radians, we know

1° = π / 180 radians

So, 5.625° = 5.625 x π/180

Taking π as 3.14, we get

5.625 x 3.14 / 180 = 0.098125 radians

Answer 2

Hello Dear.

We know that , 1' = 60''

∴ 1'' = 1/60'
∴ 30'' = 30 / 60'
         = 0.5'

∴  5°37' 30'' = 5° 37' 0.5'
 = 5°37.5'

Then, 

1' = 1/60°
∴ 37.5' = 37.5/60°
  =0.625°

Thus, 5°37'30'' = 5°+0.625°
⇒5.625° 

Now,
360°= 2π rad.
1° =π/180 rad.
∴ 5.625° = 5.625π /180 rad.
= [ 5.625 ×(22/7) ] / 180 rad.
= 17.68 /180 rad
= 0.09821 rad.

=9.821 × 10⁻² rad.

Hope it helps.
Have a nice day :-)