Two vertical poles 20 m and 80 m high stand apart on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is a' metros. Find 'a'
In △ABC and △QPC
∠BCA=∠PCQ (common)
∠CPQ=∠CBA (right angle)
So, △ABC∼△QPC (AA criteria)
Using BPT,
PQAB=CPBC⟶i
In △CBD and △PBQ
∠CBD is common,
and ∠BPQ=∠BCD (right angle)
So, △CBD=△PBQ (AAA criteria)
Using BPT, PQCD=BPBC⟶ii
Adding i and ii we get,
PQAB+PQCD=CP+BPBC=1
a20+a30=1
a=16m