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 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