Question

The angle of elevation of a cloud from a point h metres above a lake is. The angle of

depression of its reflection in the lake is 45°. The height of location of the cloud from the

lake is

(A)

1

1 –

h tan ( )

tan





+

(B)

1 -

1

h tan ( )

tan



+ 

(C) h tan (45° -) (D) none​

Answer 1

Answer:

YOUR ANSWER MATE-

Step-by-step explanation:

∠ADO=θ

Say AO=p units

∴In△AOD,tanθ=ODpOD=tanθp

Now, A′B=AB=p+hIn△A′OD,tan45°=ODA′O=ODA′B+OB=ODp+h+h

=>1=p×cotθp+2h=>p×(cotθ−1)=2h=>−p×(tanθ−1)=2h×tanθ=>p×(1−tanθ)=2h×tanθ=>p=(1−tanθ)2h×tanθ

Therefore, height of the cloud above the lake =(1−tanθ)2h×tanθ+

=(1−tanθ1+tanθ)×h=h×tan(θ+45°)

HOPE IT HELPS

STAY SAFE AND HEALTHY