From the top of a tower h m high, angle of depression of two objects, which are in line with the foot of the tower are α and β (β α). Find the distance between the two objects.

Question

From the top of a tower h m high, angle of depression of two objects, which are in line with the foot of the tower are α and β (β >α). Find the distance between the two objects.

Philoid · Accepted Answer

Given: the height of tower is h m.

∠ABD = α & ∠ACD = β

Let CD = y and BC = x

In ∆ABD,

In ∆ACD,

Comparing eq. 1 and eq. 2,

⇒ x = h (cot α – cot β)

Hence, we have got the required distance between the two points, i.e. h (cot α – cot β)