From a point 100m above a lake the angle of elevation of a 30 degree and angle of depression of its reflecting in the lake is 60 degree. find the height of helicopter.
Here is the answer to your query.
Let AB be the surface of the Lake and P be the point of observation such that AP = 100 meters. Let C be the position of helicopter and C' be its reflcation in the lake. Then CB = C'B. Let PM be perpendicular from P on CB. Then ∠CPM = 30° and ∠C' PM = 60°. Let CM = h.
Then CB = h + 100. Consequents C'B = h + 100
Then ΔCMP, we have
In ΔPMC' we have
From equation (1) and (2) we get
Now, CB = CM + MP = h + 100 = 100 + 100 = 200
Hence, the height of the helicopter from the surface of lake is 200 meters.