12. Five mark exercise problems IV

1. 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  \(km\).

 

2. The angles of elevation and depression of the top and bottom of a lamp post from the top of a \(66 \ m\) high apartment are \(60^{\circ}\) and \(30^{\circ}\) respectively. Find (i) the height of the lamp post. (ii) the difference between height of the lamp post and the apartment. (iii) the distance between the lamp post and the apartment.

 

Answer:

 

(i) The height of the lamp post \(=\)  \(m\)

 

(ii) The difference between height of the lamp post and the apartment \(=\)  \(m\)

 

(iii) The distance between the lamp post and the apartment \(=\)  \(m\)