To find angle $ \alpha $ use Law of Cosines:
$$ a^2 = b^2 + c^2 - 2 \cdot b \cdot c \cdot \cos( \alpha ) $$After substituting we have:
$$ 15^2 = 11^2 + 7^2 - 2 \cdot 11 \cdot 7 \cdot \cos( \alpha ) $$ $$ 225 = 121 + 49 - 154 \cos( \alpha ) $$ $$ 154 \cos( \alpha ) = 121 + 49 - 225 $$ $$ 154 \cos( \alpha ) = -55 $$ $$ 154 \cos( \alpha ) = -55 $$ $$ \cos( \alpha ) = -\frac{ 5 }{ 14 } $$ $$ \alpha = \arccos{ \left( -\frac{ 5 }{ 14 } \right)} $$ $$ \alpha \approx 110.9248^o $$