a man standing on deck of ship which is 10m above the sea level, observes the angle of elevation of the top of a cloud as 30 degree and angle of depression of its reflection in the sea was found to be 60 degree. find the height of the cloud and also the distance of cloud from the ship
Let AE be the height of the cloud and BD = 10m be the height of deck.
CE = BD = 10m
Let AC = h m
∴AE = AC + CE
= (h + 10) m
Now height of shadow is same
∴ AE = A' E
A' E = (h + 10) m
Now in ΔABC.
In ΔA' BC
⇒ h + 20 = 3h
⇒20 = 3h – h
⇒2h = 20
⇒h = 10 m
∴ height of the cloud = (h + 10) m
= (10 + 10) m
= 20 m
Put the value of h = 10 m in (1)
Now in ΔABC, applying Pythagoras theorem
Hence the height of the cloud is 20 m and the distance between cloud and ship is 20 m.
Let B be man, D the base of the hill, x be the distance of hill from the ship and h+10 be the height of the hill.
Substitute the value of x from equation (2) into equation (1), we have,
Height of the hill = h +10 =30 +10 =40 m
And, distance of the hill from the ship is.