Question

The angle of elevation of a cloud from a point10 m above the surface of lake is 30 degree and the angle of depression of the reflection of cloud in the lake is 60 degree find the height of cloud

Answer 1

Let AB be the surface of the lake and P be a point vertically above A such that AP = 10 m

Let C be the position of the cloud and let D be its reflection in the lake

Draw PQ perpendicular to CD then,

<QPC = 30*, <QPD = 60*,
BQ=AP =10m.
Let CQ =12cm . then
BD =BC =(x+10)m
From right triangle PQC, we have
PQ/CQ =cot 30* =root 3
=PQ/x m =root 3
=PQ =xroot3 ..... (i)

From right trianglePQD ,we have
PQ/QD=cot 60* = 1/root3

=PQ/(x+10+10)m = 1/root 3
=PQ=(x+20)/root 3 m ..... (ii)

equating values of PQ from (i) and (ii)

xroot3= (x+20)/root3

=3x=x+20
=2x=20
=x=10
height of cloud
=BC=(10+x) m
=(10+10)m
=20m

Hence height of cloud from surface of lake is 20m

is it right ??