WAEC Mathematics 2017 Theory — Question 19
Question 19 of 25 from the West African Examinations Council (WAEC) Mathematics 2017 Theory paper, with the correct answer and a full explanation.
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10(b) 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 2 significant figures: (i) Length of ladder LA; (ii) Angle which LA makes with the ground
Model answer
(i) By Pythagoras' theorem on ladder LB: |LB|²=|LM|²+|MB|², so 12²=9.6²+|MB|² → 144=92.16+|MB|² → |MB|²=51.84 → |MB|=7.2m. Then |AM|=10-7.2=2.8m. By Pythagoras on ladder LA: |LA|²=|AM|²+|LM|²=2.8²+9.6²=7.84+92.16=100 → |LA|=10m. (ii) Let θ be the angle LA makes with the ground: sinθ=9.6/10=0.96 → θ=sin^-1(0.96)≈73.74°≈74° (2 s.f.).
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