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Question Number 168737 by infinityaction last updated on 16/Apr/22

Commented by infinityaction last updated on 16/Apr/22

$find the value of x$
	Answered by mr W last updated on 17/Apr/22

	$A D = B C = 1$ $\frac{B D}{\sin 54 °} = \frac{1}{\sin 84 °}$ $\frac{\sin x}{B D} = \frac{\sin 30 °}{1}$ $\sin x = \frac{\sin 54 ° \sin 30 °}{\sin 84 °}$ $\Rightarrow x = 24 °$
	Commented by infinityaction last updated on 17/Apr/22

	$s i r s o l v e t h i s e q u a t i o n \frac{\sin 54 ° \sin 30 °}{\sin 84 °}$
	Commented by som(math1967) last updated on 17/Apr/22

	$s i n 24 \frac{s i n 54 s i n 30}{s i n 24 s i n 84}$ $s i n 24 (\frac{2 s i n 54 c o s 60}{2 s i n 24 c o s 6})$ $= s i n 24 (\frac{s i n 114 - s i n 6}{s i n 30 + s i n 18})$ $= s i n 24 (\frac{s i n 66 - s i n 6}{\frac{1}{2} + \frac{\sqrt{5} - 1}{4}})$ $= s i n 24 (\frac{2 s i n 30 c o s 36}{\frac{\sqrt{5} + 1}{4}})$ $= s i n 24 \times \frac{c o s 36}{c o s 36} = s i n 24$ $∴ s i n x = s i n 24 \Rightarrow x = 24$
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