sir this is the question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances

this is a very important question and has been asked in previous year exams.

we have been given that From a point P on the ground,

the angle of elevation of the top of a 10 m tall building

and a helicopter hovering over the top of the building are 300 and 600 respectively.

Find the height of the helicopter above the ground.

question no 15 , heights and distances , ICSE board

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 30

^{0}Â and 60^{0}We know that

Height of the building AB = 10 m

Take PA = x m and BH = h m

In right triangle ABP

tan Î¸ = P/B

Substituting the values

tan 30

^{0}Â = AB/PA = 10/xSo we get

1/âˆš3 = 10/x

x = 10âˆš3 m

In right triangle APH

tan 60

^{0}Â = AH/PAtan 60

^{0}Â = (10 + h)/ xSo we get

âˆš3 = (10 + h)/ 10âˆš3

By further calculation

10âˆš3 Ã— âˆš3 = 10 + h

30 = 10 + h

h = 30 â€“ 10 = 20

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