WAEC Mathematics 2019 Theory — Question 10

Model answer

(a) ⅓x−¼(x+2) ≥ 3x−1⅓. Multiplying through by 12: 4x−3(x+2) ≥ 36x−16 ⇒ 4x−3x−6 ≥ 36x−16 ⇒ x−6 ≥ 36x−16 ⇒ −35x ≥ −10 ⇒ dividing by −35 (reversing the inequality) x ≤ 10/35 = 2/7. (b) In ΔABC: ∠BAC=90°, ∠ACB=35°, so ∠ABC=180−90−35=55°. Using sin35°=|AB|/|BC|: |AB| = |BC|sin35° = 66×sin35° ≈ 37.86m. (i) In ΔABD: tan52° = |AD|/|AB| ⇒ |AD| = |AB|×tan52° = 37.86×tan52° ≈ 48.46m. Height of the tower = 48.46m. (ii) The angle of elevation of the top of the tower from C, ∠ACD, is found from ΔACD, using |AC| from ΔABC: cos35°=|AC|/|BC| ⇒ |AC| = |BC|×cos35° = 66×cos35° ≈ 54.06m. Then tan∠ACD = |AD|/|AC| = 48.46/54.06 ⇒ ∠ACD = tan⁻¹(0.8962) ≈ 41.87°.