Question 10
- Given that
, 00 < x < 900, find 
. - A ladder, LA, leans against a vertical pole at a point L which is 9.6 metres above the ground. Another ladder, LB, 12 metres long, leans on the opposite side of the pole and at the same point L. if A and B are 10 metres apart and on the same straight line as the foot of the pole, calculate, correct to two significant figures, the:
(i) length of ladder LA;
(ii) angle which LA makes with the ground.
Observation
The Chief Examiner reported that majority of the Candidates’ that attempted this question did very well but a few had problems in part (b) and also in approximation. The report suggested that the more emphasis should be laid on Approximation while teaching by Mathematics Teachers.
In part (a), Candidates’ who attempted this question did as expected by finding the adjacent side which is 
= 12, 
. Then substituting to have 
and simplifying yields 
.
In part (b), few Candidates’ had problem in representing the information in a diagram. They were expected to respond thus:
From the diagram, /BP/ = 
; /AP/ = 10 – 7.2 = 2.8 metres and then length of ladder LA = 
= 10 metres.
Furthermore, in part (b)(ii), the angle which LA makes with the ground 
could have been calculated using 
. Most Candidates’ could not approximate their answers to the required degree.