A landscape is drawn to scale \(1:200\,000\), so 1 cm represents 2 km. Points \(A\) and \(B\) are mountain peaks.
Their horizontal separation \(AC\) is 4 cm on the drawing; find the actual separation.
Their actual heights are 3.2 km and 8.2 km; find \(\angle BAC\).
From ground point \(P\), \(\angle APQ=12^\circ\); find \(\angle BPQ\).
A lake has actual area \(32\text{ km}^2\); find its drawing area. Give non-exact lengths, areas and other numerical values to 3 significant figures, and angles to 1 decimal place, unless otherwise stated.