The angles of elevation of the top of a tower from two points on the same side of the tower are alph...........

Quantitative Aptitude ( CCS) Trignometry

The angles of elevation of the top of a tower from two points on the same side of the tower are α and β (α >β). If the distance between the two points is 40m, find the height of the tower.

40cotαcotβ/(tanα + tanβ)

40cotαtanβ/(tanα - tanβ)

40tanαtanβ/(tanα - tanβ)

40tanαtanβ/(tanα + tanβ)

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Explanation:

Let AB is the tower of height x m and C, D are the points where the angles of elevation of the top of the tower are β and α respectively.
Also CD = 40 m
Height & Distances
In ΔABD, tan α = AB/AD
⇒ tanα = x/AD
⇒ AD = x/tanα
In Δ ACB, tan β = AB/AC
⇒ tanβ = x/[40 + (x/tanα)]
⇒ x = 40tanβ + x(tanβ/tanα)
⇒ x(1-tanβ/tanα) = 40tanβ
⇒ x[(tanα-tanβ)/tanα] = 40tanβ
⇒ x = 40tanαtanβ/(tanα - tanβ)