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Mathematics

The ratio of the length of a vertical pole and length of its shadow on the horizontal surface is 3 : 3\sqrt{3}

Assertion(A): The angle of elevation of the sun is 60°.

Reason(R): If angle of elevation of the sun is θ, tan θ = 33=3\dfrac{3}{\sqrt{3}} = \sqrt{3} = tan 60°.

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true and R is correct reason for A.

  4. Both A and R are true and R is incorrect reason for A.

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Answer

Given, the ratio of the height of a vertical pole to the length of its shadow is 3 : 3\sqrt{3}.

The ratio of the length of a vertical pole and length of its shadow on the horizontal surface is 3 : square root of 3. Concise Mathematics Solutions ICSE Class 10.

Let AB be the pole and BC be the shadow and angle of elevation of Sun be θ.

⇒Height of a vertical poleHeight of shadow=33⇒ABBC=3⇒tan θ=3⇒tan θ=tan 60°⇒θ=60°\Rightarrow \dfrac{\text{Height of a vertical pole}}{\text{Height of shadow}} = \dfrac{3}{\sqrt{3}}\\[1em] \Rightarrow \dfrac{\text{AB}}{\text{BC}} = \sqrt{3}\\[1em] \Rightarrow \text{tan θ} = \sqrt{3}\\[1em] \Rightarrow \text{tan θ} = \text{tan 60°} \\[1em] \Rightarrow θ = 60°

∴ Both A and R are true and R is correct reason for A.

Hence, option 3 is the correct option.

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