Question

An observer standing on a bank observes the top of a tree on the opposite bank making an angle of elevation 60°.He moves 34m backward and observes the top of the tree making an angle of elevation 30°. Find the height of the tree and the width of the river.​

Answer 1

Answer:

Step-by-step explanation:

Let AB be the width of the river and BC be the tree of height h metres (say). Let D be the point 20 metres away from the bank of the river and let AB=x metres.

In  ABC,

tan 60o =   =   h = x … (1)

In  DBC,

tan 30o =  … (2)

From (1) and (2),

x =

3x = x + 20

x = 10

Thus, the breadth of the river is 10 metres.

OR

Let the distance between the two towers AB and CD is 140m.

DE = CB = 140 m

Height of the second tower CD = 60 m

Let the height of first tower, AB, be h m.

CD = BE = 60 m

AE = (h - 60) m

In  AED,

= tan 30o

h - 60 = 140

h = 140 + 60

h=

h= 80.83+60 = 140.83m

Thus, the height of the first tower is 140.83 m.