The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves
20 m towards the tower, the angle of elevation of the top increases by 15°. Find the height of
the tower.
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Let AB be the tower and C and D be the point of observation
Given CD =20 m And ∠BCA=30
0
and ∠BDA=30+15=45
0
Let height of tower is h
In triangle BAD
tan45
0
=
AD
AB
⇒1=
AD
h
⇒AD=h
In triangle BAC
tan30
0
=
AC
AB
( AC=CD+AD)
⇒
3
1
=
20+h
h
⇒
3
h=20+h⇒
3
h−h=20
⇒h(1.732−1)=20
⇒h=
0.732
20
=27.3
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