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  • A man standing on the deck of a ship, which is 10 m above water level, observe the angle of elevation of the top of aa hell as 60 degree and the angle of depression of the base of the hill as 30 degree. Find the distance of the hill from the ship

A man standing on the deck of a ship, which is 10 m above water level, observe the angle of elevation of the top of aa hell as 60 degree and the angle of depression of the base of the hill as 30 degree. Find the distance of the hill from the ship and the height of the hill.

 

 

 

 
 
 
 
 

Answers (1)

Height of the deck = AB = 10m

\angle EAD = 60 \degree \\\\ \angle ACB = 30 \degree \\\\ let\: \: \: DE = x

Height of hill from ground = CE 

CE = CD+ DE 

CE = 10 + x ---- (1)

In \: \: \Delta ABC \\\\ \tan 30 \degree = \frac{AB}{BC} \\\\ \frac{1}{\sqrt3}= \frac{10}{BC } \\\\ BC = 10 \sqrt3 \\\\ NOW , BC = AD = 10 \sqrt3\\\\ In , \Delta ADE \\\\ \tan 60 \degree = \frac{DE }{AD} \\\\ \sqrt 3 = \frac{x }{10 \sqrt3}

x = 10 \sqrt3 \times \sqrt 3 = 30 \\\\ x = 30 m

Now form equation one 

CE = 10 + x \\\\ CE = 10 + 30 = 40 cm

The distance of hill from ship = BC = 10 \sqrt 3 m

Height of the hill from base = CE = 40 m 

Posted by

Ravindra Pindel

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