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What is the angle of elevation of sun when the length of shadow of a vertical pole is equal to its height?

Heights & Distances

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Answer

Let MP be the height of pole and OM be the length of shadow of pole.

What is the angle of elevation of sun when the length of shadow of a vertical pole is equal to its height? Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Given, height of pole (MP) = shadow of pole (OM) = h metres.

Let the angle of elevation be θ

In △OMP, ∠OMP = 90°.

From △OMP, we get

⇒tan θ=MPOM⇒tan θ=hh⇒tan θ=1⇒tan θ=tan 45°∴θ=45°.\Rightarrow \text{tan θ} = \dfrac{MP}{OM} \\[1em] \Rightarrow \text{tan θ} = \dfrac{h}{h} \\[1em] \Rightarrow \text{tan θ} = 1 \\[1em] \Rightarrow \text{tan θ} = \text{tan } 45° \\[1em] \therefore θ = 45°.

Hence, the angle of elevation of sun is 45°.

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