Question

4. An observer is on a tree of height x m. Which is on the bank of a river and he observed a flying plane in the angle of elevation aº at the same time he also observed the image of the plane in river water in the anlge of depression bº. For this data draw a figure​

Answer 1

Step-by-step explanation:

Let AB represent the tree of height, h metre BC be the width of the river, x m.C and D are the two different positions of the observer.

In right angle △ABC,

tan∠ACB=tan60

∘

=

BC

AB

∴h=x

3

∴

3

1

= x+30

h

∴x+30=h

3

∴h= 3

x+30

.... (ii)

From equation (i) and (ii), we get

x

3

= 3

x+30

∴x×

3×3

=x+30

∴3x=x+30

∴2x=30

∴x=15

∴ Width of the river =15 m.

Substituting the value of x in equation (i)

h=x

3

∴h=15× 3

=15×1.73

=25.95

∴ height of the tree =25.95 m.