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

Answer:60m

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/√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

diagram given down:-