A tower subtends an angle α at a point A in the place of its base and the angleof depression of the foot of the tower at a point b ft. just above A is β.Prove that the height of the tower is b tanα cotβ.

Question

A tower subtends an angle α at a point A in the place of its base and the angleof depression of the foot of the tower at a point b ft. just above A is β.Prove that the height of the tower is b tanα cotβ.

Philoid · Accepted Answer

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Let x be the distance of the point A from the foot of the tower and h be the height of the tower.

In Δ APQ,

h = x tanα …… (i)

In Δ PRB

b = x tanβ …… (ii)

From (i) and (ii),

h = b.tanα /tanβ

= b.tanα cotβ

Therefore the height of the tower is b tanα cotβ.