A man on a deck of a ship 12m above water level observes the angle of elevation of the top pf a cliff is 60degree and the angle of depression of the base of the cliff is 30degree. Find the distance of the cliff from the ship and the height if the cliff .

Let AB be the deck of the ship. AB = 10 cm

Suppose CE be the cliff. C and E are the top and bottom of the cliff.

Let CE = h m.

Given, ∠EAD = 60° and ∠DAC = 30° . 

CD = AB = 12 m

∴ DE = CE – CD = (h – 12) m

In ΔADE,

In ΔADC,

From (1) and (2), we have

Height of the cliff = 48 m

Distance of cliff from the ship = BC = AD =

  • 61

AB is the deck.

DC is the hill and AE is perpendicular to CD.

<DAE=60

<EAC=<ACB=30.

AB = 8.

in triangle abc,

AB/BC = tan30 = 1/(root3)

8/BC = 1/(root 3)

BC= 8*(root 3) metres.........(distance of the hill from the ship)

BC=AE= 8*(root 3)

in triangle ADE,

DE/AE = tan60

DE/(8*root3) = root3

DE = 24 metres.

height of the hill = DE + AC

= 24 + 8

32 METRES.

...

 

  • -7

 just place 12 m instead of 8 m

  • -9

 actually i cant give u the diagram!!but lemme explain u

draw angle of elevation 60 and angle fof depp as 30 and the height of the ship frm the ground to be 12m and the above height to be H by equating v ll get as 12+h/x=root3

and 12/x=1/root3

root3=h+12

1/root3=12/x

x=12 root3

36=h+12

h=24m

  • -14

 hw can u place 12 instead of 8???

  • -14

 I need a diagram friends .. ! ...

  • -16
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