Question

an aeroplane flying horizontally 1 km above the ground and going away from the observer is observed at an elevation of 60 degree after 10 secs ,it's elevation is observed to be 30 degree,find the uniform speed of the aeroplane in km per hour.. please don't spam ....​

Answer 1

Answer:

Let O be the point of observation and A be the position of the aeroplane such that ∠AOC=60

∘

and AC=1km

After 10seconds, let B be the position of the aeroplane such that ∠BOD=30

∘

and BD=1km

In right angled triangle,△AOC,

tan60

∘

=

OC

AC

⇒

3

=

OC

1

⇒OC=

3

1

In right angled triangle,△ODB,

tan30

∘

=

OD

BD

⇒

3

1

=

OD

1

⇒OD=

3

Now, CD=OD−OC=

3

−

3

1

=

3

3−1

=

3

2

Distance covered by the aeroplane in 10 seconds=

3

2

km

Time taken=10secs=

3600

10

=

360

1

hrs

Speed of the aeroplane=

Time

Distance

=

360

1

3

2

=

3

720

3

=240×1.732=415.68km/hr,