# Two persons are a 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 elevation of their tops to be complementary, then the height of the shorter person isA. B. C. D.

Let AB be the line joining the distance between two persons. Given C is the midpoint of AB so AC = a/2 and CB = a/2

Height of taller person is double the height of shorter person which is 2h and h respectively forming complementary angles

tan x = ……………..1

And tan 90- x =

cot x= ………………2

Multiplying 1 and 2

tan x cot x = ×

a2 = 8 h2

a = 2√2 h

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