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 nows makes with the ground.
Explanation
(a)
(b) From the above diagram,
(sin 37° = frac{5}{|LM|})
(|LM| = frac{5}{sin 37})
(|LM| = frac{5}{0.6018})
= (8.308 m)
(approxeq 8.31 m)
(cos 37 = frac{|AM|}{|LM|})
(|AM| = 8.308 times cos 37)
(|AM| = 8.308 times 0.7986)
(|AM| = 6.6348 m)
(c) The new |AM| = 6.6348 m – 2 = 4.6348 m
(cos y = frac{4.6348}{8.308})
(cos y = 0.5579)
(y = cos^{-1} (0.5579))
(y = 56.089°)
(y = 56°) (to the nearest degree).