A tower is surmounted by a vertical flag post of height 20m At a point on the ground the angle of el...........

Quantitative Aptitude ( CCS) Trignometry

A tower is surmounted by a vertical flag post of height 20m. At a point on the ground, the angle of elevation of the bottom and the top of the flag post are 30⁰ and 60⁰ respectively. Find the height of the tower.

10m

12m

16m

18m

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Explanation:

Let AB is the tower of height x m and BC is the flag post of height 20m.
In ΔABD, tan 30⁰ = AB/AD
⇒ 1/√3 = x/AD
⇒ AD = √3x ---(1)
In ΔADC, tan 60⁰ = AC/AD
⇒ √3 = (x + 20)/AD
⇒ AD = (x + 20)/√3 ---(2)
Heights & Distance Probs
From (1) & (2) we have
(x + 20)/√3 = √3x
⇒ x + 20 = 3x
⇒ 2x = 20
⇒ x = 10m
∴ The height of the tower is 10m.