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)`

Answer 1

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