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Some Applications of Trigonometry · Class 10 · CBSE Mathematics

From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30^circ. The height of the tower is:

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

easy · MCQ · Q-22B53B

From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30∘30^\circ. The height of the tower is:

  1. A.403 m40\sqrt{3}\text{ m}
  2. B.403 m\frac{40}{\sqrt{3}}\text{ m}Correct answer
  3. C.203 m20\sqrt{3}\text{ m}
  4. D.40 m40\text{ m}

Solution

Let hh be the height of the tower. In the right triangle, tan⁡(30∘)=h40\tan(30^\circ) = \frac{h}{40}. Since tan⁡(30∘)=13\tan(30^\circ) = \frac{1}{\sqrt{3}}, we get h=403 mh = \frac{40}{\sqrt{3}}\text{ m}.

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