QUESTION 4
- A man standing 3 m away from a tree observed that the angle of elevation of the top of the tree and the angle of depression of the bottom of the tree are 65o and 20o respectively. Find, correct to 3 significant figures, the height of the tree.
Observation
The Chief Examiner reported that majority of the candidates who attempted this question performed well in part (a) but poorly in part (b).
In part (a), majority of the candidates were reported to expand and simplify correctly but some of them, however, did not reverse the sign of the inequality when multiplying both sides of the sign by a negative number. Candidates were expected to remove the fraction by multiplying through by the LCM which was 12 to obtain
8(1 – 4x) – 6(5 – 3x) ≤ 3(7 + 9x) - 4.
Expanding and bringing like terms together gave -39 ≤ 41x. This implied that x ≥-
.
In part (b), candidates were expected to represent the given information in a diagram such as
Using the diagram, |TQ| = |SR| = 3 m. This implied that |PQ| = 3tan 65o and |QR| = 3tan 20o. Therefore, Height of tree = |PR| = |PQ| + |QR| = 3tan 65o + 3tan 20o = 7.53 m, correct to 3 significant figures.