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Man standing on the deck of …

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Man standing on the deck of a ship which is 10m above the water level ,observe the angle of elevation of the top of a hill as 60degree,and the angle of depression of the base of the hill as 30degree.find the distance of the hill from ship and the hight of the ship

Posted by Rashi Sharma 4 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 4 years, 11 months ago

The point of observation is at A.

The height of the deck is 10 meters.

Thus, AB = CD = 10 meters

The top and bottom of a hill is E and C.

Therefore the angles of elevation and the depression are .

Let AD = BC = x meters.

Consider the triangle ADE.

Thus,

;

Now consider the triangle ABC.

Substitute the value of x from equation (2) in equation (1), we have

Therefore

h = 30 meters .....(4)

The height of the hill is CE

That is,

Substitute the value of h from equation (4) in equation (5), we hve

Thus, the height of the hill is 40 meters and the distance of the hill from the ship is

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