Question 18528: Two towers face each other separated by a distance d = 30 m. As seen from the top of the first tower, the angles of depression of the second tower's base and top are 60 degrees and 30 degrees, respectivley. What is the height of the second tower?
Answer by kapilsinghi(68)   (Show Source):
You can put this solution on YOUR website! let the height of smaller tower ab = x
let the height of larger tower cde = x + y
distance between two towers ac and bd = 30m
cb = ad
try to see a right angled triamgle bce, right angled at c
with one side as the large tower ce,
second side as the distance between towers cb,
the third side joinng the top of large tower and base of small tower
angle ebc = 60 degrees
so tan 60 = ce/bc
= (x+y)/30
root3 = (x+y)/30
30root3 = (x+y) -------1
similarly in triangle ade right angled at d
tan 30 = y/30
1/root3 = y/30
y = 30/root3
y = (30*root3)/(root3*root3)
y = (30*root3)/3
y = 10*root3 ----------2
from 1 and 2
30root3 = (x + 10*root3)
=> 20root3 = x
x= height of small building = 20root3 = 34.64m
x+y = height of larger building = 30root3 = 51.96m
i am not able to post the diagram over here you can ask for it by mail
kapilsinghi123@gmail
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