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Draw a rough diagram according to
the problem given,
A |
|
| E l
l l
I Dl
--------------C------------
B 1 1
Join A and E to D ,
Let the height of the minor boy = DE = h m
the height of the Adult = AB = 4h m
Distance between them = BC = 2m
BC = CD = 1 m
i ) In triangle ABC ,
Angle ACB = x
< ABC = 90
Tan x = AB / BC
Tan x = 4h /1 ---------( 1 )
ii ) in triangle ECD,
Angle ECD = 90 - x ( since completary angles )
< EDC = 90
Tan ( 90 - x ) = ED / CD
Cot x = h / 1 ------( 2 )
Multiply ( 1 ) and ( 2 ), we get,
Tan x Cot x = 4h × h
1 = 4h^2
1/4 = h^2
h^2 = 1/4
h = 1/2 m
Therefore,
Height of the boy = h = 1/2 = 0.5 m
Height of the adult = 4h = 4 × 0,5 = 2 m
I hope this helps you.
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