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The angle of elevation of the top T of a vertical tower TA from point B on the ground is 60° . from a point C , 40 m vertically above the point B , angle of elevation is 30° Find the height of the tower & the distance between the points A & B.

The angle of elevation of the top T of a vertical tower TA from point B on the ground is 60° . from a point C , 40 m vertically above the point B , angle of elevation is 30° Find the height of the tower & the distance between the points A & B.

Grade:10

1 Answers

Neelesh Kumar
45 Points
3 years ago
first a fall construct the diagram
let 
TA-BC=X
NOW tan60 = (BC+(TA-BC))/AB................................(1)
SIMILARLY tan30 = (TA-BC)/AB.................................(2)
FROM equation  ..2... AB =  X * root3...............tan 30 =1/root3.......................(3)
from equation ..1   …....AB(root3) = 40 + X.............................(4)
from eq 3 put value of AB into eq 4
we get
3(X) = 40 + X
2(X) = 40
X  =  20
THEN HEIGHT OF TOWER BE   X  + 40
   20+40=60
AND DISTANCE B/W AB =20(root3)
 

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