Solve this question

Refering to the given figure-

BC = a
BD = b
As the angle of elevations are complementary to each other, their sum is = 90^o

In triangle ABC-
tan(90 - x)^o = AB/BC = AB/a
cot x^o = AB/a
tan x^o = a/AB ....(1)


In triangle ABD-
tan x^o = AB/BD = AB/b ..........(2)

From 1&2-
a/AB = AB/b
ab = (AB)²
(ab)^1/2 = AB