The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30\^{\circ}. If the angle of depression of the image of C in the lake from the point P is 60\^{\circ},then PC (in m) is equal to :
Solutions · 1
Official solution
Let PA = x
For \[\Delta \]APC
\[AC = {{PA} \over {\sqrt 3 }} = {x \over {\sqrt 3 }}\]
AC1=AB+BC1
\[A{C^1} = 200 + {x \over {\sqrt 3 }}\]
From \[\Delta {C^1}PA, \]
\[A{C^1} = \sqrt 3 PA\]
\[ \Rightarrow \left( {200 + {x \over {\sqrt 3 }}} \right) = \sqrt 3 x \]
\[\Rightarrow x = (200)(\sqrt 3 )\]
From \[\Delta APC, \]
sin 30o = \[{{{x \over {\sqrt 3 }}} \over {PC}}\]
\[ \Rightarrow \] \[PC = {{2x} \over {\sqrt 3 }} \]
\[\Rightarrow PC = 400\]