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Question Number 125632 by Mathgreat last updated on 12/Dec/20

	Answered by snipers237 last updated on 13/Dec/20

	$C o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \Rightarrow {s i n}^{2} (\frac{A}{2}) = \frac{1 - c o s A}{2} = \frac{a^{2} - {(b - c)}^{2}}{4 b c} < \frac{a^{2}}{4 b c}$ $s o 0 < s i n (\frac{A}{2}) < \frac{a}{2 \sqrt{b c}}$ $s a m e l y p r o v e t h a t 0 < s i n (\frac{B}{2}) < \frac{b}{2 \sqrt{a c}} s n d 0 < s i n (\frac{C}{2}) < \frac{c}{2 \sqrt{a b}}$ $T h e n t i m e e a c h m e m b e r .$ $L e t F o r Y o u T o C o n c l u d e .$
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