Q3 of 31 Page 122

A 1.5 metre tall boy saw the top of a building under construction at an elevation of 30°. The completed building was 10 metres higher and the boy saw its top at an elevation of 60° from the same spot. What is the height of the building?

Let x m be actual height of building and BD be the height of


boy i.e. BD = 1.5 m.


Let the distance between the boy and the building be y m.



In right Δ DFC,
FC = AC – AF = (x – 1.5) m and FD = AB = y m


FC = tan 60° × FD
⇒ (x – 1.5) = tan 60° × y
(From table, tan 60° = 1.732 )
⇒ (x – 1.75) = 1.732× y …(i)


In right Δ DFG,
FG = AC – CG – AF = (x – 10 – 1.5) m = (x – 11.5) m
and FD = AB = y m


FG = tan 30° × FD


⇒ (x – 11.5) = tan 30° × y
(From table, tan 30° = 0.57)


⇒ (x – 11.5) = 0.57 × y …(ii)


Dividing eq. (i) from eq. (ii)



⇒ 1.732(x – 11.5) = 0.57(x – 1.75)


⇒ 1.732(x) – 1.732(11.5) = 0.57(x) – 0.57(1.75)


⇒ 1.732(x) – 0.57(x) = 1.732(11.5) – 0.57(1.75)


⇒ (1.732 – 0.57)x = 19.918 – 0.9975


⇒ 1.162(x) = 18.92



Height of the building is 16.28 m.


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