# Two posts are k metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then find the height (in metres) of the shorter post.

2
by shivam2000

2015-03-13T14:14:22+05:30
|D
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A|                                                                           |   2x                                            |                                                                           |
|                                                                           |
x  |                                                                           |
|                                                                           |                                               C |................k/2................B................k/2...............| E
<---------------------------------k-------------------------->
join the point A to B and B to D  to make Δ
let <ABC = α  and <DBE = 90 - α
in ΔABC
tanα = AC/BC = x/(k/2)
tanα = 2x/k  ----------------(1)
in ΔDBE
tan(90-α) = DE/BE = 2x/(k/2)
cotα = 4x/k
1/tanα = 4x/k
put the value of tanα from the (1) equation
1/(2x/k) = 4x/k
k/2x = 4x/k
8x² = k²
x² = k²/8
x = k/2√2  meter

2015-03-13T14:22:51+05:30
Dc=2*ab
ae=ec

angle e=x
then angle aeb= 90-x
so angle aeb= 1/tanx

look into the triangle edc
tan x=
=...(1)

look into the triangle bae
tan
...(2)

1=2