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Mathematics

The angle of elevation of the sun when the length of the shadow of a pole is equal to its height, is:

  1. 30°

  2. 45°

  3. 60°

  4. 90°

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Answer

The angle of elevation of the sun when the length of the shadow of a pole is equal to its height, is: Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Let the height of the pole AB be h and length of shadow BC be s.

Given,

h = s

In triangle ABC,

⇒tan⁡θ=perpendicularbase⇒tan⁡θ=hs⇒tan⁡θ=hh⇒tan⁡θ=1⇒tan⁡θ=tan⁡45∘⇒θ=45∘.\Rightarrow \tan \theta = \dfrac{\text{perpendicular}}{\text{base}} \\[1em] \Rightarrow \tan \theta = \dfrac{h}{s} \\[1em] \Rightarrow \tan \theta = \dfrac{h}{h} \\[1em] \Rightarrow \tan \theta = 1 \\[1em] \Rightarrow \tan \theta = \tan 45^{\circ} \\[1em] \Rightarrow \theta = 45^{\circ}.

Hence, option 2 is the correct option.

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