Question

A man on the deck of a ship, 16 m above water level, observes that the angle of elevation and depression respectively of the top and bottom of a cliff are 60° and 30°. Calculate the distance of the cliff from the ship and height of the cliff. [Take `sqrt(3) = 1.732`.]

Answer 1

Let AB be the deck of the ship above the water level and DE be the cliff.

Now, 

AB  = 16msuch that CD = 16mand ∠BDA = 30° and ∠EBC = 60°
If AD = xmand DE = hm, then CE = (h-16)m.

In the right ΔBAD,we have

`(AB)/(AD) = tan 30° = 1/ sqrt(3)`

`⇒16/x = 1/ sqrt(3)`

` ⇒x = 16 sqrt(3)=27.68m`

In the right ΔEBC,we have:

`(EC)/(BC) = tan 60^0 = sqrt(3)`

`⇒((h-16))/x = sqrt(3)`

`⇒ h - 16 = xsqrt(3)`

`⇒ h - 16=16 sqrt(3) xx sqrt(3) = 48                  [ ∵ x = 16 sqrt(3)]`

`⇒ h = 48+16 = 64 m`

∴ Distance of the cliff from the deck of the ship = AD = x = 27.68m

And,
Height of the cliff = DE = h =64m