General Mathematics Paper 2,Nov/Dec. 2010
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Question 4

1.

48o

D

A

C

O

In the diagram, O is the centre of the circle,  is parallel to ,  is a straight line and  ∠OCA = 48o. Calculate ∠ABC.

1. From a window of a building, the angle of elevation of the top of a tower 50 m away is 31o and the angle of depression of the foot of the tower is 25o. Calculate, correct to 2 decimal places, the height of the tower.

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Observation

This question was reportedly poorly attempted by majority of the candidates.
In part (a), it was reported that majority of the candidates did not apply the circle theorems correctly. Candidates were expected to show that ∠BCA = 90o. Hence, ∠BCO = 90o – 48o = 42o. Thus, ∠ABC = ∠BCO = 42o (base angles of isosceles triangle BOC).
In part (b), it was reported that candidates’ inability to interpret the question correctly affected their being able to draw the diagram correctly. Some candidates did not draw it at all. As a result, they were unable to apply the trigonometric ratios correctly.

Candidates were expected to draw the diagram thus:

31o

C

h1

B

25o

50 m

A

h2

D

From the diagram, the height of the tower would be h1 + h2 = 50 tan31o + 50 tan25o              = 53.36 m.