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A tower subtends an angle $α$ at a point $A$ on the same level as the foot of the tower $B$ is a point vertically above $A$ and $AB = h$ meters. The angle of depression of the foot of the tower from $B$ is $β$ . The height of the tower is

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h tanα cotβ

htanα tanβ

h cotα cotβ

h cotα tanβ

answer is D.

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Detailed Solution

It is given that the tower subtends an angle

α

at a point .
The foot of the tower is

B

which vertically above

A

and

AB = h

meters.
The angle of depression of the foot of the tower from

B

β

.
According to the given data the figure has been drawn below.
Question Image

ΔDEB,

tan θ = P e r p e n d i c u l a r b a s e

tanα = \frac{ED}{BE}

= \frac{h}{x}

….(1)
In

ΔADC,

tan θ = P e r p e n d i c u l a r b a s e

tanβ = \frac{CD}{AD}

= \frac{h_{1}}{x}

…..(2)
Dividing the equation (1) by (2) we get,

\Rightarrow \frac{tanα}{tanβ} = \frac{h}{h_{1}}

{\Rightarrow h}_{1} = h \frac{tanβ}{tanα}

= htanβcotα

∵ tan θ = 1 cot θ

So the height of the tower is

h tanβ cotα

.
So, the correct option is 4.

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