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NDA 2019 Maths · Mathematics · Heights and Distances · easy

A kite is flying at the end of a straight string 100 m long, which makes an angle of 60^° with the horizontal ground. Neglecting the sag, the height…

Single correct option

A kite is flying at the end of a straight string 100100 m long, which makes an angle of 60∘60^\circ with the horizontal ground. Neglecting the sag, the height of the kite is
  1. A. 5050 m
  2. B. 50350\sqrt3 m
  3. C. 1003100\sqrt3 m
  4. D. 1003\dfrac{100}{\sqrt3} m
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Answer: (B) 50350\sqrt3 m

The string is the hypotenuse and the height is the side opposite the 60∘60^\circ angle. So h=100sin⁡60∘=100×32=503h=100\sin60^\circ=100\times\dfrac{\sqrt3}{2}=50\sqrt3 m. The value 5050 would apply for 30∘30^\circ, where sin⁡30∘=12\sin30^\circ=\dfrac12. Using tan⁡\tan instead of sin⁡\sin confuses the string with the horizontal distance.
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Original question written in the NDA 2019 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