Question

If the angle of elevation of a loud from a
point 'h'metres above a Lake is o, and the
angle of depression of its reflection is the
lake 92. prove that the height that the
cloud 13 Located from the ground is
h etano,+tan oz)
tan oz-tano,​

Answer 1

Answer:

hlo here is ur answer mate ❣️

Step-by-step explanation:

✔️✅Let AB be the surface of the lake and let C be a point of observation such that AC = h metres Let D be the position of the cloud and D be its reflection in the lake Then BD = BD

In Δ DCE

tanα=CEDE⇒CE=tanαH............(i)

In Δ CED'

⇒CE=tanβh+H+h⇒CE=tanβ2h+H............(ii)

From (i) & (ii)

⇒tanαH=tanβ2h+H⇒Htanβ=2htanα+Htanα

Htanβ−Htanα=2htanα⇒H(tanβ−tanα)=2htanα

⇒H=tanβ−tanα2htanα.........(iii)

In Δ DCE sinα=CDDE⇒CD=sinαDE⇒⇒CD=sinαH

Substituting the value of H from (iii) 

CD=(tanβ−tanα)sinα2htanα