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The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

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Answer

From figure,

Let AB be the tower.

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower. NCERT Class 10 Mathematics CBSE Solutions.

In △ABC,

tan 30° = Side opposite to angle 30°Side adjacent to angle 30°\dfrac{\text{Side opposite to angle 30°}}{\text{Side adjacent to angle 30°}}

Substituting values we get :

⇒13=ABBC⇒13=AB30⇒AB=303⇒AB=103 m.\Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{AB}{BC} \\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{AB}{30} \\[1em] \Rightarrow AB = \dfrac{30}{\sqrt{3}} \\[1em] \Rightarrow AB = 10\sqrt{3} \text{ m}.

Hence, height of tower = 10310\sqrt{3} m.

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