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Example 7
The angle of elevation of a cloud from a point
100m above a lake is 300 and the angle of depression
of its reflection in the lake 600. Find the height of
the cloud.
Solution : C = cloud, LM = surface of the lake.
C' = reflection of the cloud.
\ CM = MC'
Ð NOC =
300 and ÐNOC' = 600
Also OL = NM = 100 m
Let CM = x and ON = a
then C'N = C'M + MN
\ C'N = x + 100.
Also CN = CM - NM = x - 100
Again from the right triangle ONC,
 
\ 3 (x - 100) = x + 100 \
3x - 300 = x + 100 \ 2x = 400 \
x = 200
\The height of the
cloud above the surface of the lake is 200m.
Example 8
Using the fig. below find x and y and the area
of the triangle.
Solution : In triangle ABC, B = C = 65
\ triangle ABC is an isosceles.
\ AB = AC i.e. x = y
seg AD ^ side BC
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