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A tower subtends at angle $θ$ at a point P on the same level as the foot of the tower and from a point h m above P the depression of the foot of the tower is $α$ . Evaluate the height of the tower in metres.

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h

tanθtanα

h

cotθcotα

h

tanθcotα

cotθtanα

answer is C.

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Detailed Solution

It is given that a tower subtends at angle

θ

at a point P on the same level as the foot of the tower and from a point h m above P the depression of the foot of the tower is

α

Let H be the height of the tower.
Here,

nθ = \frac{H}{x}

.
⇒

x = Hcotθ . . . . . (1)

tanα = \frac{h}{x}

⇒

x = hcotα . . . . . (2)

Equating (1) and (2), we get,
⇒

Hcotθ = hcotα

⇒

H = hcotαtanθ

Hence, the correct option is 3.

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