Question

10 degree 40 minutes 30 seconds can be expressed in radian as:​

Answer 1

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Clearly , 30" = (30/60)'

$= > \: ( \frac{1}{2})min$

Now 40'30" can be written as :-

$= > \: 40 \frac{1}{2} min.$

$= > \: \frac{81}{2} min$

Now we have to convert min . value in degree so :-

$= > \: \frac{81}{2} \times \frac{1}{60}$

$= > \: \frac{27}{40} degree \:$

So 10° 40'30" = 10 ×(27/40)°

$= > \: 10 \times \frac{27}{40} = \frac{27}{4}$

Now we know that to convert degree measure in radian we multiple it with π/180 , So

$= > \: \frac{27}{4} \times \frac{\pi}{180}$

$= > \: \frac{3\pi}{80} radian$

$\huge\mathfrak{Thanks}$