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Mathematics

The ratio of the length of a rod and its shadow is 1 : 3\sqrt{3}. The angle of elevation of the sun is:

  1. 30°

  2. 45°

  3. 60°

  4. 90°

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Answer

The ratio of the length of a rod and its shadow is 1. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

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

In triangle ABC,

tanθ=perpendicularbasetanθ=hstanθ=13tanθ=tan30θ=30.\Rightarrow \tan \theta = \dfrac{\text{perpendicular}}{\text{base}} \\[1em] \Rightarrow \tan \theta = \dfrac{h}{s} \\[1em] \Rightarrow \tan \theta = \dfrac{1}{\sqrt3} \\[1em] \Rightarrow \tan \theta = \tan 30^{\circ} \\[1em] \Rightarrow \theta = 30^{\circ}.

Hence, option 1 is the correct option.

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