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.
Now consider the triangle ABC.
Substitute the value of x from equation (2) in equation (1), we have
h = 30 meters .....(4)
The height of the hill is CE
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
Let B be man, D the base of the hill, x be the distance of hill from the ship and h+10 be the height of the hill.
Substitute the value of x from equation (2) into equation (1), we have,
Height of the hill = h +10 =30 +10 =40 m
And, distance of the hill from the ship is.