This question was previously asked in

Territorial Army Paper I : Official Practice Test Paper - 1

Option 3 : 12

**Given**

The distance between two pillars of length 16 m and 9 m is x meters.

Two angles of elevation of their respective top from the bottom of the other are complementary to each other.

**Concept used**

If two angles of elevation are complimentary to each other then H = √ab

Where a and b are the Length of the pillars.

**Calculation**

AB and CD are two pillars of Length 16 m and 9m.

Let the angle of elevation at B and D be θ and (90 - θ)

Distance between two pillars BD be x metres

IN Δ ABC

Tanθ = AB/BD = 16/x - - - -(i)

In Δ BDC

Tan(90 - θ) = CD/BD = 9/x

Cotθ = 9/x - - - - (ii)

Multiply equation i and ii

⇒ Tanθ × Cotθ = (16/x) (9/x)

⇒ 144/x^{2} = 1

⇒ x^{2} = 144

⇒ **x = 12 m**

**Second Method**

If two angles of elevation are complimentary to each other then H = √ab

Where a and b are the Length of the pillars.

H = \(\sqrt {16 \times 9} \)

H = √144

H = 12 m