The angle of elevation from the foot of a building to the top of a tower is 60°. The angle of depression from the top of the same building to the foot of the tower is 30°. What is the ratio of their heights?
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Answer:
Let AB be the hill and CD be the tower.
Angle of elevation of the hill at the foot of the tower is 60
o
, i.e., ∠ADB=60
o
and the angle of depression of the foot of hill from the top of the tower is 30
o
, i.e., ∠CBD=30
o
.
Now in right angled ΔCBD:
tan30
o
=
BD
CD
BD=
tan30
o
CD
BD=
3
1
50
BD=50
3
m
In right ΔABD:
tan60
o
=
BD
AB
AB=BD×tan60
o
AB=50
3
×
3
AB=50×3
AB=150 m
Hence, the height of the hill is 150 m.
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