1(xii)
An observer at point E, which is at a certain distance from the lamp post AB, finds the angle of elevation of top of lamp post from positions C, D and E as α, β and γ. It is given that B, C, D and E are along a straight line.
Which of the following conditions is satisfied ?
- (a)tan α > tan β
- (b)tan β < tan γ
- (c)tan γ > tan α
- (d)tan α < tan β
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From figure,
⇒ tan α = $\frac{AB}{BC}$
⇒ tan β = $\frac{AB}{BD}$
⇒ tan γ = $\frac{AB}{BE}$
Since, BC < BD < BE.
∴ tan α > tan β > tan γ.
∴ tan α > tan β.
Hence, Option 1 is the correct option.