Mathematics class 10

Question

The angle of elevation of an aeroplane from a point A on the ground is 60°. After a

flight of 15 seconds horizontally, the angle of elevation changes to 30°. If the aeroplane

is flying at a speed of 200m/s, then the constant height at which the aeroplane is flying.

Answer 1

In case- I

h/x=tan60 and h/(3-x)=tan30

So (3-x)/x=√3/(1/√3)=3

=>3-x=3x

=>x=3/4=0.75km

And h=√3x=√3×0.75km=1.3km

Case-Ii

h/y=tan60 and h/(y+3)=ta30

(y+3)/y=3

=>3y=y+3

=>y=3/2=1.5km

Hence h=y×tan60=1.5×√3=2.6km