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An electric pole is 10 metres high. If its shadow is 10310\sqrt{3} metres in length, find the elevation of the sun.

Heights & Distances

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Answer

Let the angle of elevation be θ as shown in the figure below:

An electric pole is 10 metres high. If its shadow is 10√3 metres in length, find the elevation of the sun. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Consider △ABC, AB be the height of electric pole and BC be the shadow. Since pole and it's shadow are perpendicular, ∠ABC = 90°.

From △ABC, we get

⇒tan θ=ABBC⇒tan θ=10103⇒tan θ=13⇒tan θ=tan 30°∴θ=30°.\Rightarrow \text{tan θ} = \dfrac{\text{AB}}{\text{BC}} \\[1em] \Rightarrow \text{tan θ} = \dfrac{10}{10\sqrt{3}} \\[1em] \Rightarrow \text{tan θ} = \dfrac{1}{\sqrt{3}} \\[1em] \Rightarrow \text{tan θ} = \text{tan 30°} \\[1em] \therefore \text {θ} = 30°.

Hence, the elevation of the sun is 30°.

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