33. Five mark exercise problem IX

Three villagers \(A\), \(B\) and \(C\), can see each other across a valley. The horizontal distance between \(A\) and \(B\) is \(8 \ km\), and the horizontal distance between \(B\) and \(C\) is \(12 \ km\). The angle of depression of \(B\) from \(A\) is \(20^{\circ}\), and the angle of elevation of \(C\) from \(B\) is \(30^{\circ}\). Calculate (i) the vertical height between \(A\) and \(B\). (ii) the vertical height between \(B\) and \(C\). (\(tan \ 20^{\circ} = 0.3640\), \(\sqrt{3} = 1.732\))

 

 

Answer:

 

(i) The vertical height between \(A\) and \(B\) is  \(km\).

 

(ii) The vertical height between \(B\) and \(C\) is \(km\).