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Mathematics

If the angle of depression of an object from a 75 m high tower is 30°, then the distance of the object from the tower is

  1. 25325\sqrt{3} m

  2. 50350\sqrt{3} m

  3. 75375\sqrt{3} m

  4. 150 m

Heights & Distances

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Answer

From figure,

If the angle of depression of an object from a 75 m high tower is 30°, then the distance of the object from the tower is. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

∠ACB = ∠DAC = 30° (Alternate angles are equal)

Considering right angled △ABC we get,

⇒tan 30°=ABBC⇒13=75BC⇒BC=753\Rightarrow \text{tan 30°} = \dfrac{AB}{BC} \\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{75}{BC} \\[1em] \Rightarrow BC = 75\sqrt{3}

Hence, Option 3 is the correct option.

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