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Question
From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. Find the height of the second tree. `(sqrt(3) = 1.732)`
Solution
Let the height of the second tree be “h”
ED = (h – 13) m
Let AB = x m
In the right ∆ABC, tan 30° = `"BC"/"AB"`
`1/sqrt(3) = 13/x`
x = `13sqrt(3)` ...(1)
In the right ∆CED, tan 45° = `"DE"/"EC"`
1 = `("h" - 13)/x`
x = h – 13 ...(2)
From (1) and (2) we get
h – 13 = `13sqrt(3)`
⇒ h = `13sqrt(3) + 13`
= 13 × 1.732 + 13
= 22.52 + 13
= 35.52 m
∴ Height of the second tree = 35.52 m
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