27. From a point on the ground, the angles of elevation of the top and bottom of
a transmission tower fixed at the top of a 20m high building are 60' and 45°
respectively. Find the height of the transmission tower.
0-60°
B
20m
009
459
D
C
-
SIOP
Answers
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Answer:
Let DC be the tower and BC be the building. Then,
∠CAB=45
o
,∠DAB=60
o
,BC=20 m
Let height of the tower, DC=h m.
In right △ABC,
tan45
o
=
AB
BC
1=
AB
20
AB=20 m
In right △ABD,
tan60
o
=
AB
BD
3
=
20
h+20
h=20(
3
−1) m
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