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Question
From a point 10 m above the ground , the angle of elevation of the top of a tower is α and the angle of depression is β . If tan α = `5/2` and tan β = `1/4` , calculate the height of the tower to the nearest metre .
Solution
Let AD be the tower and B be the point of observation.
In ΔABC,
tan ∝ = `"AC"/"BC"`
⇒ `"h"/"x" = 5/2` ....(1)
In ΔBED,
`tanβ = "BE"/"ED"`
⇒ `1/4 = 10/"x"`
⇒ x = 40
From (1),
h = 100
∴ Height of the tower = h + 10 = 100 + 10 = 110 m
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