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A student is solving this problem: 'A ladder leans against a wall making an angle of 30° with the level ground, and its foot is 6 m from the wall. Find the length of the ladder.'
The student writes: 'Length = 6 cos 30 = 3 m.'
Which statement correctly describes the mistake?

Class 10Heights and DistancesTrigonometry
  • AThe ratio has been used upside down: cos , so m; also a hypotenuse can never be shorter than the 6 m base.
  • BThe student should have used sin 30 instead of cos 30, which gives L = 3 m.
  • CThe angle should be measured from the wall instead of from the ground, which gives m.
  • DThere is no mistake; 3 m is the correct length of the ladder.

Step-by-Step Solution

The 6 m base is adjacent to the 30° angle and the ladder is the hypotenuse, so cos m (about 6.93 m). The student's 3 m is about 5.20 m, shorter than the base, which is impossible.
Answer: A) The ratio has been used upside down: cos , so m; also a hypotenuse can never be shorter than the 6 m base.

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