If the angle of elevation of a cloud from a point 200 m above a lake is 30∘ and the angle of depression of its reflection in the lake is 60∘, then the height of the could above the lake is
400 m
Let AB the height of the could above the lake be H metre. BC is the lake surface, and BQ is the distance of the reflection formed from the lake surface.
AB = BQ = H m, CD = PB = 200 m
AP = AB - PB = H - 200
PQ = PB + BQ = 200 + H
in ΔADP, tan 30∘=APPD
⇒1√3=H−200PD⇒PD=√3(H−200) ---(1)
In ΔPDQ, tan 60∘=PQPD
⇒ √3=H+200PD⇒ PD=H+200√3 --- (2)
From (1) and (2), we get
(H−200)√3=H+200√3
⇒ 3(H - 200) = H + 200
⇒ 3H - 600 = H + 200
⇒ 2H = 800 ⇒ H = 400 m