From the top of a building 15 m high the angle of elevation of the top of tower is found to be 30°. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower and the distance 34between the tower and the building.
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Answer:
- Height of the tower = 22.5 m
- Distance between the tower & building = 12.99 m
Step-by-step explanation:
Let AB be the building & CD be the tower
Given:
- AB ( Height of the buliding ) = 15m
- Angle of elevation of the top of tower from top of the building = 30°
- Angle of elevation of the top of tower from bottom of building = 60°
To find:
- Height of the tower ( CD )
- Distance between the tower & the buliding ( BD )
Solution:
In ∆ ACE,
tan 30° = CE / AE
=> 1 / √3 = CE / AE
=> AE = √3 CE ( Equation 1 )
In ∆ BCD,
tan 60° = CD / BD
=> √3 = CD / BD
=> BD = CD / √3
But, BD = AE = Distance between the tower and building
=> AE = CD / √3 ( Equation 2 )
From equation 1 & 2, we get
√3 CE = CD / √3
=> CE = CD / 3 ( Equation 3 )
ED = AB = Height of the building = 15m
CD = CE + ED = Height of the tower
=> CD = (CD / 3) + 15
=> CD - (CD / 3) = 15
=> 2CD/3 = 15
=> CD = 15*(3/2) = 22.5m ( Height of the tower )
From equation 2, we get
AE = CD / √3
=> AE = 22.5 / √3 = 12.99 m ( Distance between the tower & building )
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