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Mathematics

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 ?

  1. tan α > tan β

  2. tan β < tan γ

  3. tan γ > tan α

  4. tan α < tan β

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. ICSE 2024 Maths Specimen Solved Question Paper.

Heights & Distances

ICSE Sp 2024

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Answer

From figure,

⇒ tan α = ABBC\dfrac{AB}{BC}

⇒ tan β = ABBD\dfrac{AB}{BD}

⇒ tan γ = ABBE\dfrac{AB}{BE}

Since, BC < BD < BE.

∴ tan α > tan β > tan γ.

∴ tan α > tan β.

Hence, Option 1 is the correct option.

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