Given: The angle of elevation of the top of a tower of height x meter from a point on the ground is found to be 60∘ By going y metre away from that point, it becomes 30∘ Concept used: tanθ=P∕B Here P= perpendicular, B= base
According to the question, tan60∘=AB∕BC ⇒√3=x∕BC ⇒BC=x∕√3 Again, tan30∘=AB∕BD ⇒1∕√3=AB∕BD ⇒1∕√3=x∕BD ⇒BD=√3x BD=BC+CD ⇒√3x=x∕√3+y [From equation (1) ⇒√3x=(x+√3y)∕√3 ⇒3x=x+√3y ⇒2x=√3y ∴ Required answer is Option 3