Question

If a person at the top of building in front of his house from the ground the angle of elevation is 60°. If he looks at the top of building from the terrace 5m height .the angle of elevation is 30°.find the height of building.

Answer 1

Answer:

|D

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| h= 5m

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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