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\includegraphics[max width=\textwidth, alt={}, center]{bbee5a50-4a32-4171-8713-8eb38914a511-3_623_355_1123_897} Some walkers see a tower, \(T\), in the distance and want to know how far away it is. They take a bearing from a point \(A\) and then walk for 50 m in a straight line before taking another bearing from a point \(B\). They find that angle \(T A B\) is \(70 ^ { \circ }\) and angle \(T B A\) is \(107 ^ { \circ }\) (see diagram).

1. Find the distance of the tower from \(A\).
2. They continue walking in the same direction for another 100 m to a point \(C\), so that \(A C\) is 150 m . What is the distance of the tower from \(C\) ?
3. Find the shortest distance of the walkers from the tower as they walk from \(A\) to \(C\).