QQuestion
The angle of elevation of the top of a pillar of height h from two points in the same horizontal line through the foot of the pillar and in the same side of the pillar are θ and φ respectively. Find the distance between two points.
✓Answer
Let the height of the pillar be h. Let the horizontal distances from the foot of the pillar to the two observation points be x and y respectively (both on the same side of the pillar).
In ΔABD,
tan φ = h/x ⇒ x = h/tan φ
In ΔABC,
tan θ = h/y ⇒ y = h/tan θ
The distance d between the two points = y – x
= h/tan θ – h/tan φ
= h(cot θ – cot φ)
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