Question

4. The two palm trees are of equal heights and are standing opposite each other on
either side of the river, which ks 80 m wide. From a polnt o between them on the river
the angles of elevation of the top of the trees are 60° and 30°, respectively. Find the
height of the trees and the distances of the point o from the trees.​

Answer 1

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Answer 2

Let BD = river

AB = CD = palm trees = h BO = x OD = 80 - x In ∆ABO, tan60˚ = h/x

√3 = h/x ---- (1)

H = √3x

In ∆CDO, tan30˚ = h/80−x

1√3 = h/80−x --- (2)

Solving (1) and (2),

we get x = 20

H = √3x = 34.6

The height of the trees = h = 34.6m BO = x = 20m

DO = 80 - x = 80 - 20 = 60m