Question

From an airplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the airplane are observed to be 30° and 60° respectively. The height at which the airplane is flying in km is :

• A. (A) 43
• B. (B) 32
• C. (C) 23
• D. (D) 2

Answer 1

Answer: (B)

(B) 32

Answer 2

Given: The angle of depression of two consecutive stones when observed from an airplane are 30∘ and 60∘.We have to find the height at which the airplane is flying.
Consider,Let, AB=h km
BC=x km and CD=1 km
Consider, right angled △ABC,
tan⁡60∘=ABBC⇒3=hx⇒x=h3.........(i)
In right angled △ABD, we have
tan⁡30∘=ABBD⇒13=hx+1⇒x+1=3 h.......(ii)
From (i) and (ii), we get
h3+1=3 h⇒h+3=3h⇒2h=3⇒h=32 km
Hence, the correct option is (B).