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Some Applications of Trigonometry · Class 10 · CBSE Mathematics

The angle of elevation of the top of a tower from a point on the ground is 30^circ. If on walking 50 meters towards the tower the angle of elevation…

Practice question from Some Applications of Trigonometry (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-50D1E8

The angle of elevation of the top of a tower from a point on the ground is 30∘30^\circ. If on walking 50 meters towards the tower the angle of elevation becomes 60∘60^\circ, then the height of the tower is:

  1. A.253 m25\sqrt{3}\text{ m}Correct answer
  2. B.503 m50\sqrt{3}\text{ m}
  3. C.253 m\frac{25}{\sqrt{3}}\text{ m}
  4. D.50 m50\text{ m}

Solution

Let height be hh and the final distance from the tower be xx. Then tan⁡(60∘)=hx  ⟹  x=h3\tan(60^\circ) = \frac{h}{x} \implies x = \frac{h}{\sqrt{3}}. The initial distance was x+50x + 50, so tan⁡(30∘)=hx+50  ⟹  13=hh3+50\tan(30^\circ) = \frac{h}{x + 50} \implies \frac{1}{\sqrt{3}} = \frac{h}{\frac{h}{\sqrt{3}} + 50}. Solving this gives h=253 mh = 25\sqrt{3}\text{ m}.

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