Question

prove that the height of a tower is 6 m when angle of elevation from top of the tower to two points 4m and 9m away from bottom of the tower is complementory

Answer 1

Figure is in the attachment.

In ABC = Tan(90-Ф) = CotФ

CotФ = AB\BC

1\TanФ = AB/BC

TanФ = BC/AB------------------(1)

In ABD

TanФ = AB/BD-------------------------(2)

From (1) and (2)

AB\BD = BC/AB

AB² = BC*BD

AB = √9*4

AB = √36

AB = 6cm

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