Question

14. From the top of a tower AB, 90 m high, the angles of depression of the top
and the bottom of
a building CD are observed to be 45° and 60°respectively. Find
i). the horizontal distance between AB and CD.
ii). the height of the building CD.
​

Answer 1

$\huge\mathcal{\fbox\red{ATQ}}$

The height of building AB=60 m.

And angle of the depression of the top and bottom of vertical lamp post CD are observed to be 30

∘

and 60

∘

, respectively shown in the figure.

In the △ADB,

tan60

∘

=

x

60

3

=

x

60

x= 3

60m

In the △ACP,

tan30 ∘= x60−h

31=3

60

60−h

3

60

=60−h

h=60−20

h=40 m

Therefore,

The distance of between AB and CD is

3

60

m.

The height of lamp post is 40 m.

The difference between the height of the building and the lamp post =60−40=20 m.