The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
30m
40m
20m
10m
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EXPLANATION.
Let building be AB
Let tower be CD
- GIVEN
height of tower = 60m
CD = 60m
Angle of elevation of top of building from
foot of tower = 30°
<ACB = 30°
Angle of elevation of top of tower to foot of building = 60°
<DBC = 60°
TO FIND HEIGHT OF BUILDING.
in a right angle triangle <DBC
Tan B = DC / BC
√3 = 60 / BC
BC = 60 / √3
similarly in right angle triangle ABC
Tan c = AB / BC
1/√3 = AB / 60 / √3
1/√3 X 60 / √3 = AB
60/3 = AB
AB = 20 m
Hence,
Height of building = 20m
THEREFORE,
OPTION [C] IS CORRECT
NOTE = FOR DIAGRAM SEE THE ATTACHMENT IMAGE.
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