Question

The angles of elevation of a pillar from point A and B are respectively 30° and 60°. If the distance between A and B is l, then the difference of point A and the foot of the pillar is :

(A) l(1 + √3/2)

(B) (√3/2)l

(C) 3l/2

(D) None of these

Answer 1

Answer is (C) 3l/2

Let PQ is pillar of height h. 

Let point B is at x distance from foot of pillar Q.

According to question,

∠PAQ = 30°, ∠PBQ = 60° and AB = l

From right angled ΔPQB,

tan 60° = PQ/BQ

⇒ √3 = h/x

⇒ h = √3 x …..(i)

From right angled ΔPQA,

tan 30° = PQ/AQ

⇒ 1/√3 = h/(l + x)

⇒ l + x = √3h

⇒ l + x = √3(√3x) [From equation (i) h = √3x]

⇒ l + x = 3x

⇒ 2x = l

⇒ x = l/2

Hence, distance between foot of pole and point A.

= AQ = AB + BQ

= l + x

= l + l/2 

= 3l/2