Answer
$\dfrac {\sqrt {7}}{4}$
Work Step by Step
$\sin \left( \arccos x\right) =\sqrt {1-x^{2}}\Rightarrow \sin \left( \arccos \dfrac {3}{4}\right) =\sqrt {1-\left( \dfrac {3}{4}\right) ^{2}}=\dfrac {\sqrt {7}}{4}$
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