Answer
2.5 km
Work Step by Step
With east as +x, north as +y,
$\vec{AB}=(25km)\hat{i},\quad \vec{BA}=(-25km)\hat{i}$
$\vec{AC}=(24km)(\cos(-15^{o})\hat{i}+\sin(-15^{o})\hat{j})+(8.0km)\hat{j}$
Then;
$\vec{BC}=\vec{BA}+\vec{AC}=$
$=[-25+24(\cos(-15^{o})) km ]\hat{i}\\+[(8.0+24(\sin(-15^{o}))km]\hat{j}$
$=(-1.8km)\hat{i}+(1.8km)\hat{j}$
Thus, the magnitude $\sqrt{1.8^{2}+1.8^{2}}=2.5$ km
