Question

13. When one end of a ladder, LM, is placed against a vertical wall at a point 5 metres above the ground, the ladder makes an angle of 37° with the horizontal ground.
(a) Represent this information in a diagram.
(b) Calculate, correct to 3 significant figures, the length of the ladder.
(c) If the foot of the ladder is pushed towards the wall by 2 metres, calculate, correct to the nearest degree, the angle which the ladder now makes with the ground.

Accepted Answer

(a) The diagram shows a right-angled triangle formed by the vertical wall, the horizontal ground, and the ladder LM as the hypotenuse; the ladder touches the wall at a height of 5m, and makes an angle of 37° with the ground at its foot.

(b) sin37° = MF/ML (where MF=5m is the height on the wall, ML is the ladder length). ML = MF/sin37° = 5/0.6018 = 8.31m (3 s.f.).

(c) Using tan37° = MF/LF: LF = MF/tan37° = 5/0.7536 = 6.64m (the original horizontal distance from the foot of the ladder to the wall). If the foot is pushed 2m closer to the wall, the new horizontal distance UF = LF−2 = 4.64m. The ladder length ML=8.31m remains the same (it doesn't change length). Using cosθ = UF/ML = 4.64/8.31 = 0.5584. θ = cos⁻¹0.5584 = 56° (nearest degree) — the new angle the ladder makes with the ground.

WAEC Mathematics 2013 Theory — Question 14

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