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NDA 2023 Maths · Mathematics · Heights and Distances · easy

A 10 m long ladder leans against a vertical wall and makes an angle of 60^° with the horizontal ground. The height of the point where the ladder…

Single correct option

A 1010 m long ladder leans against a vertical wall and makes an angle of 60∘60^\circ with the horizontal ground. The height of the point where the ladder touches the wall is
  1. A. 55 m
  2. B. 535\sqrt3 m
  3. C. 10310\sqrt3 m
  4. D. 103\dfrac{10}{\sqrt3} m
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Answer: (B) 535\sqrt3 m

The ladder is the hypotenuse, so the height is 10sin⁡60∘=10⋅32=5310\sin60^\circ=10\cdot\tfrac{\sqrt3}2=5\sqrt3 m. Using cos⁡60∘\cos60^\circ gives the horizontal distance 55 m of the foot from the wall. Option 103\tfrac{10}{\sqrt3} wrongly applies tan⁡\tan rather than sin⁡\sin.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake