 Hello and how are you all today? The question to be discussed is a man standing on the deck of a ship Which is 10 meter above the water level observes the angle of elevation of the top of a hill as 60 degrees and the angle of depression of the base as 30 degrees What we need to do is we need to calculate the distance of the hill From the ship and the height of the hill Now this is the figure that will help us In finding the solution to this question Here what we are given is angle D a e is Equal to 60 degrees whereas angle ACB is equal to 30 degrees and We are given that the height of the deck from the water level is 10 meter So AB is equal to EC as it is forming a rectangle is equal to 10 meters We need to find the length of BCD Right, let the distance of TV edge meters Now in this we need to refer to two triangles in triangle EAD and Triangle ABC Now let us first talk about EAD We are given we need to find out the relationship between Perpendicular and base right so we will be using the relation of tan theta that is Perpendicular upon base the perpendicular we have taken as edge meters and the base is a e Further, we know that here theta is equal to 60 degrees so tan 60 degrees is equal to Edge upon let a e be x meters if a e is x meter then BC will auto automatically be x meters right now We know that the value of tan 60 degree is root 3 so on substituting the value We have root 3x is equal to Edge let this be the first equation Let us carry on with the second triangle that we have taken now here also We have tan theta is equal to perpendicular upon base now here the perpendicular is a b Whereas base is BC now theta here is given to us as 30 degrees so we have tan 30 degrees is Equal to a b that is 10 meters divided by BC that we have taken as x meters Substituting the value of tan 30 degrees as 1 by root 3 so 1 by root 3 into x or 1 by root 3 Into x is equal to 10 or X is equal to 10 root 3 now we know that the value of root 3 is Equal to 1.73 So x is equal to 17.3 meters Now we can substitute the value of x from second in the first equation we can find out the Distance of edge So we have H is equal to root 3 into x That is 1.73 as root 3 is 1.73 Into x which is 17.3 now here We have its value as 30 meters approximately that is further equal to H. We have taken as D e now here we were required to find out the value the height of the hill right so The height of the hill is 10 plus the value of H. Now what we have found out to be 30. So CD is equal to E C plus V e that is 10 meters plus 30 meters that is equal to 40 meters right so our final answer is therefore the distance of the hill from the ship is found out to be 17.3 meters and The height of the hill is 40 meters So this ends the session I was taking hope you have a great time and bye for now