Question

the angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60 degrees and the angle of elevation of the top of the second tower from the foot of the first tower is 30 degrees. find the distance between the two tower and also the height of the other tower.

Answer 1

3
The answer for your query is as follows:

 







Let the first tower be AB and the second tower be CD.
Given: AB = 30m
​angle ACB = 60o
angle DBC = 30o
Now, in right triangle ABC,
tan 60o = AB/BC
√3 = 30/BC
BC = 30/√3  
=> BC = 30√3/3            (Rationalising)
BC = 10√3m
Now in right triangle BCD,
tan 30o = CD/DB
1/√3 = CD/10√3
CD√3 = 10√3
CD = 10√3/√3
=> CD = 10m
​Therefore, the distance between the two towers is 10√3m (i.e. BC) and the height of the other tower is 10m
Hope this helps.:)

Answer 2

The height of the second tower is 90m
The distance between the two towers is 30√3m