Answer
$\approx90^0$
Work Step by Step
From the law of cosines
$\left[ AC\right] ^{2}=110^{2}+138^{2}-2\times 110\times 138\times \cos 38^{0}\approx 7220\Rightarrow \left| AC\right| \approx \sqrt {7220}\approx 84.97$
From the law of sines
$\dfrac {\left[ AC\right] }{\sin 38}=\dfrac {138}{\sin \theta }\Rightarrow \sin \theta =\dfrac {138\times \sin 38}{\left[ AC\right] }\approx 1\Rightarrow \theta \approx \sin ^{-1}\left( 1\right) \approx 90^0$
