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Home » From the top of a building 20 m high, the angle of elevation of the top of a monument is 450 and the angle of depression of its foot is 150. Find the height of the monument.
From the top of a building 20 m high, the angle of elevation of the top of a monument is 450 and the angle of depression of its foot is 150. Find the height of the monument.
ML Agarwal Heights and distances class 10 Maths
From the top of a building 20 m high, the angle of elevation of the top of a monument is 450 and the angle of depression of its foot is 150. Find the height of the monument.

Solution:

Consider AB as the building where AB = 20 m

CD as the monument where CD = x m

Take the distance between the building and the monument as y

In right triangle BCD

tan θ = CD/BD

Substituting the values

tan 450 = x/y

1 = x/y

x = y …… (1)

In right triangle ABD

tan 150 = AB/BD = 20/x

Substituting the values

0.2679 = 20/x

So we get

x = 20/0.2679 = 74.65 m

Hence, the height of the monument is 74.65 m.

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