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Question
A pole 6 m high casts a shadow `2sqrt(3)` m long on the ground, then the Sun’s elevation is ______.
Options
60°
45°
30°
90°
Solution
A pole 6 m high casts a shadow `2sqrt(3)` m long on the ground, then the Sun’s elevation is 60°.
Explanation:
Let BC = 6 m be the height of the pole and AB = `2sqrt(3)` m be the length of the shadow on the ground.
Let the Sun's makes an angle θ on the ground.
Now, In ΔABC,
tan θ = `"BC"/"AB"`
⇒ tan θ = `6/(2sqrt(3))`
= `3/sqrt(3) * sqrt(3)/sqrt(3)`
⇒ tan θ = `(3sqrt(3))/3`
= `sqrt(3)` ...`[∵ tan 60^circ = sqrt(3)]`
= tan 60°
∴ θ = 60°
Hence, the Sun's elevation is 60°.
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