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  • The angle of elevation of the top of a building from the foot of a tower is  and the angle of elevation of the top of a tower from the foot of the building

The angle of elevation of the top of a building from the foot of a tower is 30^{\circ} and the angle of elevation of the top of a tower from the foot of the building is 60^{\circ}. If the tower is 50 \: m high, then find the height of the building.

 

 

 

 
 
 
 
 

Answers (1)


Let the height of the building be h m
\tan 60^o = \frac{PQ}{BQ} = \frac{50}{BQ}
\\\sqrt{3} = \frac{50}{BQ}\\ BQ = \frac{50}{\sqrt{3}}.......................(i)

\tan 30^o = \frac{h}{BQ}
{BQ}=h\sqrt{3}.........................(ii)
On equating the eq(i) and (ii) we get,

\frac{50}{\sqrt{3}}=h\sqrt{3}
therefore, h = 50/3 = 16.66 m = height of the building.

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Safeer PP

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