WAEC Mathematics 1999 Theory question 109

Theory question 109

Trigonometry

In the diagram, a ladder TF, 10m long is placed against a wall at an angle of 70° to the horizontal. (a) How high up the wall, correct to the nearest metre, does the ladder reach? (b) If the foot (F) of the ladder is pulled from the wall to F¹ by 1 metre. (i) how far, correct to 2 significant figures, does the top T, slide down the wall to T¹ (ii) Calculate, correct to the nearest degree, ∠QF¹T¹.

Show the model answer

Model answer

(a) QT = 10 sin 70° = 9.397 ≈ 9 m.
(b) QF = 10 cos 70° = 3.420 m, so QF¹ = 4.420 m.
(i) QT¹ = √(10² − 4.420²) = √80.46 = 8.970 m. Slide = 9.397 − 8.970 = 0.427 ≈ 0.43 m.
(ii) cos ∠QF¹T¹ = 4.420/10 = 0.442, so the angle ≈ 64°.

Explanation

The ladder's length stays 10 m, so use Pythagoras for the new height.