Question

TWO POSTS ARE "k" METRE APART AND THE HEIGHT OF ONE IS DOUBLE THAT OF OTHER. IF FROM THE MID-POINT OF THE LINE SEGMENT JOINING THEIR FEET, AN OBSERVER FINDS THE ANGLES OF ELEVATION OF THEIR TOPS TO BE COMPLEMENTARY, THEN FIND THE HEIGHT OF THE SHORTED POST.

Answer 1

|D
|
|
|
|
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