Question

A man on the deck of a ship 14m above the water level observers that the angle of elevation of the top of a cliff is 60 degree and the angle of depression of the base of the cliff is 30 degree . Calculate the distance of the cliff from the ship and the height of the cliff

Answer 1

hey there is answer !!/


h = 56m
distance is 24.25 m


I hope you help

Answer 2

Answer:

The distance of the cliff from the ship and the height of the cliff is 24.248 m and 55.998 m respectively.

Step-by-step explanation:

Refer the attached figure :

A man on the deck of a ship 14m above the water level i.e. ED = 14 m

The angle of elevation of the top of a cliff is 60 degree i.e. ∠AEB = 60°

The angle of depression of the base of the cliff is 30 degree . i.e.∠ECD = 30°

We are supposed to find the distance of the cliff from the ship i.e. CD and the height of the cliff i.e. AC

ED = BC = 14 m

In ΔECD

$Tan 30^{\circ} = \frac{ED}{CD}$

$\frac{1}{\sqrt{3}} = \frac{14}{CD}$

$CD= \frac{14}{\frac{1}{\sqrt{3}}}$

$CD=24.248$

Now CD=BE=24.248 m

So, the distance of the cliff from the ship is 24.248 m

In  ΔABE

$Tan 60^{\circ} = \frac{AB}{BE}$

$\sqrt{3} = \frac{AB}{24.248}$

$\sqrt{3} \times 24.248  =AB$

$41.998  =AB$

Height of cliff = AB +BC = 41.998+14 =55.998 m

Hence  the distance of the cliff from the ship and the height of the cliff is 24.248 m and 55.998 m respectively.