From the top of a building 60m high the angle of elevation and depression of the top and the foot of...........

Quantitative Aptitude ( CCS) Trignometry

From the top of a building 60m high, the angle of elevation and depression of the top and the foot of another building are α and β respectively. Find the height of the second building.

60(1+ tan α tanβ)

60(1+ cot α tanβ)

60(1+ tan α cotβ)

60(1- tan αcotβ)

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Explanation:

Let AB is the building of height 60m and CD is the second building such that ∠DBE = α and ∠CBE = ∠BCA =β\

Height & Distances
In ΔBAC, tanβ = 60/AC
⇒ BE = AC = 60/tanβ = 60cotβ
In ΔBED, tan α = DE/BE ⇒ tanα = DE/60cotβ
⇒ DE = 60 cot β tan α
∴ The height of the building = CD = CE + ED
= 60 + 60 cot β tan α
= 60 (1 + tan α cot β)