3
\includegraphics[max width=\textwidth, alt={}, center]{608720b6-5b18-45e9-8838-c94b347ab3b7-2_488_604_895_769} A landmark \(L\) is observed by a surveyor from three points \(A , B\) and \(C\) on a straight horizontal road, where \(A B = B C = 200 \mathrm {~m}\). Angles \(L A B\) and \(L B A\) are \(65 ^ { \circ }\) and \(80 ^ { \circ }\) respectively (see diagram). Calculate

1. the shortest distance from \(L\) to the road,
2. the distance \(L C\).