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WAEC 2020 · Paper 2 · Q5

A ladder 10 m10\text{ m} long leans against a vertical wall at an angle of 70∘70^\circ to the ground. If the ladder slips down the wall 4 m4\text{ m}, find, correct to two significant figures:

  1. (a)

    the new angle which the ladder makes with the ground;

  2. (b)

    the distance the ladder slipped back on the ground from its original position.

Worked solution (try it first)
  1. Draw the wall vertical and the ground horizontal, with the 10 m ladder at 70∘70^\circ to the ground.
  2. At first the top of the ladder is 10sin⁡70∘≈9.39710\sin 70^\circ \approx 9.397 m up the wall, and the foot is 10cos⁡70∘≈3.42010\cos 70^\circ \approx 3.420 m from the wall.

(a)

  1. The top slips 4 m down, to 9.397−4=5.3979.397 - 4 = 5.397 m.
  2. The ladder is still 10 m long: sin⁡θ=5.39710=0.5397\sin\theta = \frac{5.397}{10} = 0.5397, so θ≈32.7∘\theta \approx 32.7^\circ, which is 33∘33^\circ to two significant figures.

(b)

  1. The foot is now 10cos⁡32.7∘≈8.41910\cos 32.7^\circ \approx 8.419 m from the wall.
  2. It slipped back 8.419−3.420≈5.08.419 - 3.420 \approx 5.0 m.

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