# If sin 2 theta = cos 3 theta, where 2 theta and 3 theta are acute angles, what is the value of theta? Answer soon plzzzzz!

$\mathrm{sin}2\mathrm{\theta }=\mathrm{cos}3\mathrm{\theta }\phantom{\rule{0ex}{0ex}}⇒\mathrm{sin}2\mathrm{\theta }=\mathrm{sin}\left(90-3\mathrm{\theta }\right)\phantom{\rule{0ex}{0ex}}⇒2\mathrm{\theta }=90-3\mathrm{\theta }\phantom{\rule{0ex}{0ex}}⇒2\mathrm{\theta }+3\mathrm{\theta }=90\phantom{\rule{0ex}{0ex}}⇒5\mathrm{\theta }=90\phantom{\rule{0ex}{0ex}}⇒\mathbf{\theta }\mathbf{=}\mathbf{18}\phantom{\rule{0ex}{0ex}}$

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