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Circles

Question
CBSEENMA10009601
Wired Faculty App

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

Solution

Let CD be the hill and suppose the man is standing on the deck of a ship at point A.

The angle of depression of the base C of the hill CD observed from A is 30° and the angle of elevation of the top D of the hill CD observed from A is 60°.
therefore angle EAD space equals space 60 degree space and space angle BCA space equals 30 degree In space increment AED comma tan space 60 degree space equals DE over EA therefore square root of 3 space equals straight h over straight x therefore space straight h equals square root of 3 straight x space space... space left parenthesis 1 right parenthesis In space increment ABC comma tan space 30 degree space equals space AB over BC therefore space fraction numerator 1 over denominator square root of 3 end fraction equals 10 over straight x therefore space straight x equals 10 square root of 3 space in space equation space left parenthesis 1 right parenthesis comma space we space get straight h equals square root of 3 space straight x 10 square root of 3 space equals space 10 straight x 3 space equals 30 therefore space DE space equals space 30 space straight m therefore space CD equals CE plus ED space equals 10 plus 30 space equals space 40 space straight m Thus comma space the space distance space of space the space hill space from space the space ship space is space 10 square root of 3 space straight m space and space the space height space of space the space hill space is space 40 space straight m.

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