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    The length of a vertical rod and its shadow are in the ratio of 2:12.2:\sqrt{12}.2:12​. Find the angle of elevation of the sun.​
    Question

    The length of a vertical rod and its shadow are in the ratio of 2:12.2:\sqrt{12}. Find the angle of elevation of the sun.​

    A.

    75°

    B.

    45°

    C.

    60°

    D.

    30°

    Correct option is D

    Given:

    Ratio of height of rod : length of shadow = 2:12 : \sqrt{12}​​

    Formula Used:

    For a vertical object and its horizontal shadow: tanθ=heightshadow\tan\theta=\dfrac{\text{height}}{\text{shadow}}​​

    Solution:
    Let the angle of elevation be θ.\theta.​​
    heightshadow=212\dfrac{\text{height}}{\text{shadow}}=\dfrac{2}{\sqrt{12}}​​

    =223=13=\dfrac{2}{2\sqrt{3}}=\dfrac{1}{\sqrt{3}}​​

    tanθ=13 \tan\theta=\dfrac{1}{\sqrt{3}}​​
    θ=30. \theta=30^\circ.​​

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