An observer finds that the angular elevation of a tower is θ. On...

An observer finds that the angular elevation of a tower is

\theta.

On advancing

3m

towards the tower, the elevation is

{45}^{o}

and on advancing

2m

further more towards the tower, the elevation is

{90}^{o} - \theta.

The height of the tower is (assume the height of observer is negligible and observer lies on the same level as the foot of the tower) An observer finds that the angular elevation of a tower is θ. On advancing 3m towards the tower, the elevation is 45 ^

An observer finds that the angular elevation of a tower is θ. On advancing 3m towards the tower, the elevation is 45 ^

Options

A $2m$
B $4m$
C $6m$
D $8m$

Correct answer

C. $6m$

Step-by-step solution

Let,

PQ

be the tower of height

h

meters

∠PAQ = \theta, ∠PBQ = {45}^{o}

and

∠PCQ = {90}^{o} - \theta

AB = 3m

and

BC = 2m

⇒ 3 = AB = PA - PB = hcot A - h

and

2 = BC = PB - CP = h - htan A

∴ \dfrac{h + 3}{h} = cot A, \dfrac{h - 2}{h} = tan A

∴ \dfrac{h + 3}{h} \cdot \dfrac{h - 2}{h} = 1 ⇒ h^{2} + h - 6 = h^{2} ⇒ h = 6m

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