Solution:

Consider AB as the building and H as the helicopter hovering over it

P is a point on the ground

Angle of elevation of the top of building and helicopter are 30⁰ and 60⁰

We know that

Height of the building AB = 10 m

Take PA = x m and BH = h m

In right triangle ABP

tan θ = P/B

Substituting the values

tan 30⁰ = AB/PA = 10/x

So we get

1/√3 = 10/x

x = 10√3 m

In right triangle APH

tan 60⁰ = AH/PA

tan 60⁰ = (10 + h)/ x

So we get

√3 = (10 + h)/ 10√3

By further calculation

10√3 × √3 = 10 + h

30 = 10 + h

h = 30 – 10 = 20

Height of the helicopter from the ground = 10 + 20 = 30 m