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 the hill as 60° and the angle of depression of the base of the hill is 30°. Calculate the distance of the hill from the ship and the height of the hill.
Answers
Answer:
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
Answer:
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