Question

Two persons on the same side of a tall building notice the angle of elevation of the top of the building to be 30degree and 60degree respectively. If the heights of elevation of the top of the building is 72m , find the distance between two persons .(underroot 3=1.7)

Answer 1

|D
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A------------------------------B----------------------C
x y
let CD is the building and A & B are the two person. join the point A with D and B with D. from A elevation is 30 degree and from B elevation is 60 degree.
AB = distance between two person = x m
in triangle ACD
tan 30 = CD/AC
1/√3 = 60/AC
AC = 60√3
x+y = 60√3 -----------------(1)
in triangle BCD
tan 60 = CD/BC
√3 = 60/BC
BC = 60/√3
y = 60/√3
put the value of y in equation (1)
x + 60/√3 = 60√3
x = 60√3 - 60/√3
x = 60(3-1)/√3
x = 120/√3
x = 40√3 meter