Math, asked by santdehar1322, 10 months ago

find the value of (420°)

Answers

Answered by yashmalaiya2006

The value of (420°) is 7.44

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{ \frac{22}{3} \: radians}$

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

an $\angle = 420°$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

radian measure

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Conservation of units

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

We know that,

$2\pi \: rad = 360°$

$\Rightarrow 1° = \frac{\pi}{180} rad$

Therefore,

$\Large{420° = (420 \times \frac{\pi}{180} )rad}$

$\Large{ \: \: \: \: \: \: \: \: \: \: = (420 \times \frac{ \frac{22}{7} }{180} )rad}$

$\Large{ \: \: \: \: \: \: \: \: \: \: = (420 \times \frac{22}{7 \times 180} )rad}$

$\Large{ \: \: \: \: \: \: \: \: \: \: = ( {}^{6} \cancel{42} \cancel{0} \times \frac{ \cancel{22} {}^{11} }{ \cancel{7} \times _9 \cancel{18} \cancel{0} } )rad}$

$\Large{ \: \: \: \: \: \: \: \: \: \: = \frac{6 \times 11}{9} \: rad}$

$\Large{ \: \: \: \: \: \: \: \: \: \: = \frac{{ \cancel{6} }^{2} \times 11}{ \cancel{9} _3} \: rad}$

$\Large{ \: \: \: \: \: \: \: \: \: \: = \frac{22}{3} \: rad}$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

$420° = \frac{22}{3} \: rad = 7.33 \: radians$

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