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A vertical pole is 12 m high and the length of its shadow is 12312\sqrt{3} m. What is the angle of elevation of the sun?

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A vertical pole is 12 m high and the length of its shadow What is the angle of elevation of the sun?.Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Let AB be the height of pole = 12 m.

Length of shadow BC = 12312\sqrt{3} m

In triangle ABC,

⇒tan⁡θ=perpendicularbase⇒tan⁡θ=12123⇒tan⁡θ=13⇒tan⁡θ=tan⁡30°⇒θ=30°.\Rightarrow \tan \theta = \dfrac{\text{perpendicular}}{\text{base}} \\[1em] \Rightarrow \tan \theta = \dfrac{12}{12\sqrt3} \\[1em] \Rightarrow \tan \theta = \dfrac{1}{\sqrt3} \\[1em] \Rightarrow \tan \theta = \tan 30° \\[1em] \Rightarrow \theta = 30°.

Hence, angle of elevation of the sun is 30°.

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