From a point 100m above a lake the angle of elevation of a 30 degree and angle of depression of - Maths - Some Applications of Trigonometry

Question

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

Aakash Sharma · Accepted Answer

Dear Student! 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 $\tan 30 ° = \frac{CM}{PM} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{PM} \Rightarrow PM= \sqrt{3} h$ In ΔPMC' we have $\tan 60 ° = \frac{C'M}{PM} = \frac{C'B+BM}{PM} \Rightarrow \sqrt{3} = \frac{h + 100 + 100}{PM} \Rightarrow PM= \frac{h + 200}{\sqrt{3}}$ From equation (1) and (2) we get $\sqrt{3} h = \frac{h + 200}{\sqrt{3}} \Rightarrow 3 h = h + 200 \Rightarrow 3 h - h = 200 \Rightarrow 2 h = 200 \Rightarrow h = \frac{200}{2} = 100$ Now, CB = CM + MP = h + 100 = 100 + 100 = 200 Hence, the height of the helicopter from the surface of lake is 200 meters Cheers!

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.