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Question
The lengths of a vertical rod and its shadow are in the ratio `1 : sqrt(3)`. The angle of elevation of the sun is ______.
Options
30°
45°
60°
90°
MCQ
Fill in the Blanks
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Solution
The lengths of a vertical rod and its shadow are in the ratio `1 : sqrt(3)`. The angle of elevation of the sun is 30°.
Explanation:
Let AB be the rod of length x metres and let AC be its shadow of length `(sqrt(3)x)` m.
Let ∠ACB = θ.
Then, `(AB)/(AC) = tan θ`
⇒ `tan θ = x/(sqrt(3)x) = 1/sqrt(3)`
⇒ tan θ = tan 30°
⇒ θ = 30°
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