Construct an angle whose sine is (3/(2 + (√5))) .


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Question Number 206971 by MATHEMATICSAM last updated on 02/May/24

$Construct an angle whose sine is$ $\frac{3}{2 + \sqrt{5}} .$
	Answered by Rasheed.Sindhi last updated on 02/May/24

	$\sin θ = \frac{3}{2 + \sqrt{5}}$ $∙ θ i s a n a n g l e o f a r i g h t t r i a n g l e$ $w h o s e h y p o t e n u s e i s 2 + \sqrt{5} a n d$ $o p p o s i t e s i d e i s 3$ $∙ \sqrt{5} i s a h y p o t e n u s e o f a r i g h t$ $t r i a n g l e h a v i n g l e g s 2 a n d 1$ $▸ D r a w a r i g h t t r i a n g l e h a v i n g$ $l e g s 2 a n d 1 . E x t e n d i t s h y p o t e n u s e$ $\sqrt{5} t o \sqrt{5} + 2 .$ $D r a w s e m i c i r c l e o n l i n e s e g m e n t$ $\overset{―}{AB} h a v i n g m e a s r e \sqrt{5} + 2$ $C u t o f f 3 u n i t s f r o m B o f s e m i c i r c l e$ $a t C .$ $J o i n C t o A a n d B$ $∠ BAC i s a r e q u i r e d a n g l e .$
	Commented by Rasheed.Sindhi last updated on 02/May/24

	Commented by MATHEMATICSAM last updated on 02/May/24

	$Thank you!$
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