Question

AN AEROPLANE AT AN ALTITUDE OF 200M OBSERVES THE ANGLE OF DEPRESSION OF OPPOSITE POINTS ON THE 2 BANKS OF A RIVER TO BE 45DEGREE AND 60 DEGREE. FIND IN METRES THE WIDTH OF THE RIVER.

Answer 1

Hi ,

Draw a rough diagram of given data

|A
|
|
| 60
|__________|___________45_
B. C. D

Join A to C and D

Let

Height of the aeroplane from the

ground = AB = 200m



Width of the river = CD

i) In right triangle ABD,

tan 45° = AB / BD

1 = 200 / BD

BD = 200m ---( 1 )

ii ) In triangle ABC ,

Tan 60° = AB / BC

√3 = 200 / BC

BC = 200 /√3

BC =( 200 √3)/( √3 × √3 )

BC = 200√3 / 3----( 2 )

iii ) width of the river =

CD = BD - BC

= 200 - 200√3/3

= 200( 1 - √3 /3)

= 200( 3 - √3 )/3

=( 200/3) ( 3 - √3 ) m

I hope this helps you.

:)

Answer 2

hope it will help you.....