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Question
If a pole 12 m high casts a shadow `4sqrt(3)` m long on the ground then the sun’s elevation is ______.
Options
60°
45°
30°
90°
MCQ
Fill in the Blanks
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Solution
If a pole 12 m high casts a shadow `4sqrt(3)` m long on the ground then the sun’s elevation is 60°.
Explanation:
Let AB be the pole and AC be its shadow.
AB = 12 m and `AC = 4sqrt(3) m`.
Let ∠ACB = θ.
Then, `tan θ = (AB)/(AC) = 12/(4sqrt(3))`
⇒ `tan θ = 12/(4sqrt(3)) xx sqrt(3)/sqrt(3)`
⇒ `tan θ = sqrt(3)`
⇒ tan θ = tan 60°
⇒ θ = 60°
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