Question

The two palm trees are of equal heights and are standing opposite each
other on either side of the river, which is 80 m wide. From a point 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

Step-by-step explanation:

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/√13 = 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