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Question
From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is
Options
25 m
50 m
75 m
100 m
Solution
Given that: height of cliff is 25 m and angle of elevation of the tower is equal to angle of depression of foot of the tower that is θ.
Now, the given situation can be represented as,
Here, D is the top of cliff and BE is the tower.
Let CE = h, `AB=x`. Then, `AB=DC`= = x
Here, we have to find the height of the tower BE.
So, we use trigonometric ratios.
In a triangle ABD,
`⇒ tan θ= AD/AB`
`⇒ tan θ=25/x` (1)
Again in a triangle,`DCE`
`tan θ=(CE)/(CD)`
`⇒ tan θ=h/x`
`⇒25/x=h/x` [using 1]
`⇒h=25`
Thus, height of the tower = BE = BC + CE = (25 + 25) m = 50 m
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