Theory question 113
TrigonometryWhen 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.
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(a) Right triangle: wall 5 m, ladder LM as hypotenuse, 37° between ladder and ground.
(b) |LM| = 5/sin 37° = 5/0.6018 ≈ 8.31 m.
(c) Original foot distance = 5/tan 37° ≈ 6.64 m; new distance = 4.64 m. The ladder length stays 8.31 m: cos θ = 4.64/8.31 ≈ 0.558, so θ ≈ 56°.
When the foot moves, the ladder slides up the wall; its length does not change.