A man looks up at a pole making angle of elevation is 45°. When he looks at the reflection of the tip of the pole in water, he finds the angle of depression as 60°. If the man is 1 m tall, find height of the pole.
Explanation:
EA is the line representing the ground.
Height of the man (represented by AB) = 1 meter.
Let height of the pole (ED) = x meters.
In ∆BFD, tan45° = 1 = DF/BF
⇒ BF = DF …(1)
In ∆BFD, tan60° = √3 = CF/BF
⇒ BF = CF/√3 …(2)
From (1) and (2)
DF = CF/√3
⇒ x – 1 = (x + 1)/√3
⇒ √3x - √3 = x + 1
⇒ √3x - x = 1 + √3
⇒ x = (√3 + 1)/(√3 - 1)
⇒ x = (√3 + 1)2/2
⇒ x = (4 + 2√3)/2 = 2 + √3
Hence, option (c).
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