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.

Let us observe the following figure.

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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