Mast and pillar from a midpoint
Question
A communications tower and a flagpole stand on the same horizontal ground. From the point O, midway between the foot of the flagpole, S, and the foot of the tower, T, the angle of elevation of the top of the tower, G, is 65°. From the same point O, the angle of elevation of the top of the flagpole, H, is 25°. The flagpole is 8 m high.
- Represent the information in a diagram.
- Calculate, correct to the nearest whole number:
- the height of the tower;
- |HG|.
What examiners reported
On the original question, most candidates never produced a usable diagram. Without it they could not see the two right-angled triangles sharing the point O. The few who drew it correctly found both answers without trouble.
Model answer
Where marks are lost
O is between S and T. Put them on opposite sides and the two triangles appear.
H and G are also apart horizontally by the whole of ST, so |HG| is a hypotenuse.
Carry four decimal places through the working and round only at the end.
Sample unit. Mark allocations are being reviewed by experienced WASSCE examiners before launch.