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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Heights and Distances

NTA Abhyas 2020 · Mathematics · Heights and Distances

The angle of elevation of an object on a hill is observed from a...

The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 30°30 °. After walking 120m120m towards it on a level ground, the angle of elevation is found to be 60°60 °. Then the height of the object (in metres) isThe angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its

Options

  1. A120120
  2. B60360\sqrt{3}
  3. C1203120\sqrt{3}
  4. D6060

Correct answer

B. 60360\sqrt{3}

Step-by-step solution

In ∆CAD,tan⁡30°=CDAC∆ CAD,\tan 30 ° = \dfrac{CD}{AC}

The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its

⇒13=h120+x⇒ \dfrac{1}{\sqrt{3}} = \dfrac{h}{120 + x}

⇒3h=120+x⇒ \sqrt{3}h = 120 + x...(i)

and in∆CBD∆ CBD, tan⁡60°=CDBC\tan 60 ° = \dfrac{CD}{BC}

⇒3=hx⇒h=3x⇒ \sqrt{3} = \dfrac{h}{x} ⇒ h = \sqrt{3}x...(ii)

From Eqs. (i) and (ii), we get, x=60mx = 60m

On putting x=60x = 60 in Eq.(i), we get

h=603mh = 60\sqrt{3}m
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