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Mathematics

If a pole 6 m high casts shadow 232\sqrt{3} m long on the ground, then the sun's elevation is

  1. 60°

  2. 45°

  3. 30°

  4. 90°

Heights & Distances

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Answer

Let the angle of elevation be θ and AB be the pole.

If a pole 6 m high casts shadow 2√3 m long on the ground, then the sun's elevation is. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Considering right angled △ABC we get,

⇒tan θ=623⇒tan θ=33⇒tan θ=3⇒tan θ=tan 60°⇒θ=60°.\Rightarrow \text{tan θ} = \dfrac{6}{2\sqrt{3}} \\[1em] \Rightarrow \text{tan θ} = \dfrac{3}{\sqrt{3}} \\[1em] \Rightarrow \text{tan θ} = \sqrt{3} \\[1em] \Rightarrow \text{tan θ} = \text{tan 60°} \\[1em] \Rightarrow θ = 60°.

Hence, Option 1 is the correct option.

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