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A surveyor whose eyes are 1.6 m above the ground stands on level ground 30 m from the foot of a communication tower in Raipur.
From her eye level the angle of elevation of the top of the tower is 45°.
She writes: 'Height of the tower = 30 tan 45 = 30 m.'
What is wrong with her answer?

Class 10Heights and DistancesTrigonometry
  • ANothing is wrong; the height of the tower is 30 m.
  • BShe should have used sin 45, so the height is m.
  • CShe should have subtracted her eye height, so the height is 28.4 m.
  • DShe has found only the part of the tower above her eye level; her eye height of 1.6 m must be added, giving 31.6 m.

Step-by-Step Solution

The right triangle she used has its horizontal side at eye level, 1.6 m above the ground, so 30 tan 45 = 30 m is the height of the tower ABOVE HER EYES. The full height of the tower = 30 + 1.6 = 31.6 m.
Answer: D) She has found only the part of the tower above her eye level; her eye height of 1.6 m must be added, giving 31.6 m.

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