Question

The angle of elevation of an aircraft from a point k on the horizontal ground is 30. If the aircraft is from above the ground /how far is it from x ?

Answer 1

Step-by-step explanation:

Let P and Q be the two positions of the aircraft and A be the point of observation.

Let ABC be the horizontal line through A.

It is given that angles of elevation of the aircraft in two positions P and Q from a point A are 60 and 30 respectively.

So,∠PAB=60 ,∠QAC=30

°

PB=3600 √3m

In ΔABP,

tan60

°

=BP/AB

√3 =3600 √3 /AB

AB=3600 m

In ΔACQ,

tan30

°

=CQ/AC

1/ √3=3600 √3 /AC

AC=3600 √3 × √3

AC=3600×3

AC=10800 m

Distance =BC=AC–AB

BC=(10800–3600) m

BC=7200 m

Speed of aircraft =7200 m /24 sec

=300 m/sec

OR

=(300/1000)×60×60 km/hr

=(3/10)×3600 km/hr

Speed of aircraft =1080 km/hr

Note [1 km =1000 m, 1 hr =60 min =60×60