Question

A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.

Answer 1

The distance of the cliff from the ship is 17.32 m

The height of the cliff is 27.32 m

Explanation:

Given that the man on the deck of a ship is 10 m above the water level.

The angle of elevation of the top of a cliff from the ship deck is 45° and the angle of depression of the base is 30°.

We need to find the distance of the cliff from the ship and the height of the cliff.

From the figure, we have,

$BE=CD=10$ , $\angle \mathrm{ABC}=45^{\circ}$ and $\angle \mathrm{DBC}=30^{\circ}$

Let the distance of the cliff from the ship be BC

Let the height of the cliff be AD

Let us consider the ΔABC,

$tan \ 45^{\circ}=\frac{AC}{BC}$

         $1=\frac{AC}{BC}$

     $BC=AC$ -------(1)

Let us consider the ΔBCD,

$tan \ 30 ^{\circ}=\frac{CD}{BC}$

       $\frac{1}{\sqrt{3}}=\frac{10}{B C}$

      $B C=10 \sqrt{3}$

      $BC=17.32 \ m$

Thus, the distance of the cliff from the ship is 17.32 m

Equating $BC=17.32 \ m$ in equation (1), we have,

$BC=AC=17.32$

Height of the cliff is given by

$A D=A C+CD$

      $=17.32+10$

$AD=27.32 \ m$

Thus, the height of the cliff is 27.32 m

Learn more:

(1) A man standing on the deck of a ship, which is 10m above the water level, observes the angle of elevation of the top of a hill as 60 degree and the angle of depression of the base of the hill as 30 degree. Find the distance of the hill fom the ship and the height of the hill.

brainly.in/question/1001119

(2) A man standing on the deck of a ship, 10 m above the water level observes the angle of elevation of the top of a hill as 60° and angle of depression the bottom of a hill as 30°. Find the distance of the hill from the ship and height of the hill.

brainly.in/question/3036191