#### Answer

$BC=\dfrac {76\times \sin \angle A}{\sin \angle C}=\dfrac {76\times \sin 27.2}{\sin 115.5}\approx 38.49;$
$AC=\dfrac {76\times \sin \angle B}{\sin \angle C}=\dfrac {76\times \sin 37.3}{\sin 115.5}\approx 51.03$

#### Work Step by Step

$\dfrac {76}{\sin \angle C}=\dfrac {BC}{\sin \angle A}=\dfrac {AC}{\sin \angle B};\angle B=180-\angle A-\angle C=180-27.2-115.5=37.3\Rightarrow $
$BC=\dfrac {76\times \sin \angle A}{\sin \angle C}=\dfrac {76\times \sin 27.2}{\sin 115.5}\approx 38.49;AC=\dfrac {76\times \sin \angle B}{\sin \angle C}=\dfrac {76\times \sin 37.3}{\sin 115.5}\approx 51.03$